United produced a stunning second half display to come back from two goals down at the break to bag a deserved point against Chelsea at Stamford Bridge.
Callum Robinson's cross was turned in to his own net by Zouma with just a minute of normal time remaining to send the away end into delirium.
It was no more than the Blades deserved after an impressive second half showing which saw Robinson reduce the arrears just after the break, after Chelsea raced into a 2-0 lead.
Boss Wilder gave Oli McBurnie a first Premier League start for the club, making just one change to the side which last started a top flight fixture against Leicester City. David McGoldrick dropped to the bench which also included fellow striker Mousset who impressed midweek against Blackburn Rovers.
Both sides enjoyed spells of possession during the opening four minutes, as the game took time to get going. The hosts upped the ante though on six minutes when a ball over the top temporarily had Tammy Abraham in behind, but the Blades quickly recovered to clear through Jack O'Connell. Soon after a cross from the Chelsea right was met by Ross Barkley but the England midfielder failed to time his header with his attempt a long way off target.
United then had the Chelsea defence under pressure for the first time as Enda Stevens' left wing cross was deflected behind for a corner, but Ollie Norwood's near post delivery was headed clear by Abraham.
On 15 minutes Fikayo Tomori sailed a long pass in behind the United defence for Abraham to chase. Despite suspicions of offside, play went on but the striker dragged his shot comfortably wide of the far post.
Three minutes later United registered an effort from distance after McBurnie won the ball back high up the pitch. Norwood then played a short pass into the feet of Luke Freeman who arrowed a shot on the turn wide of the near post.
With little in terms of goalmouth action, the hosts took the lead on 19 minutes with the first meaningful effort of the game. A cross from the right was headed towards goal by Abraham, but Dean Henderson failed to collect cleanly due to the presence of Christian Pulisic, with the loose ball stabbed into the net by Abraham.
United were then forced to soak up some pressure, but had an opportunity at the other end on 25 minutes. Stevens crossed from the left with Kurt Zouma's clearing header falling straight into the path of Chris Basham who blazed over with a shot from 20 yards.
The Blades showed class in the final third just before the half hour mark as neat and patient interplay between Stevens, O'Connell and Robinson created half an opening for Freeman, whose strike towards goal on the angle was blocked.
Chelsea were a whisker away from making it 2-0 on 37 minutes as Mateo Kovacic drove into the United area with a purposeful run but his low shot slipped inches past the far post.
Moments later United were almost level. John Lundstram lifted a pass into the right channel which was seized upon by Basham. His early low centre looked to have caught out the Chelsea defence with Robinson the quickest to react, but his glancing diving header fell agonisingly wide.
With just three minutes of the first half remaining Chelsea benefitted from a communication error as O'Connell and John Egan both attempted to head Jorginho's chipped pass. The loose ball was seized upon by Abraham who drove the ball home for his second, despite the best efforts of Henderson.
The Blades could have conceded a third before the break as Mason Mount saw a sight of goal, but a useful deflection took the ball wide.
The goal came at a time when United looked to be getting a foothold in the game, and the frustration was too much for McBurnie who was cautioned on the stroke of half-time for dissent.
The United half-time chat had an immediate effect as the Blades pulled one back on 46 minutes. Stevens had the Chelsea defence on the ropes as he glided past two defenders with a break down the left, he then cut the ball back for ROBINSON who netted with a cool first-time side-footed finish to celebrate in front of the travelling Blades supporters.
United had Henderson to thank for staying just one behind as Azpilicueta's centre was seized upon by Abraham, but the Blades' number one produced a fine save low to his right to deny the striker, with Lundstram also putting in a fine challenge to deny any shots from the rebound.
A swift counter attack by the Blades then saw McBurnie turn the ball in behind for Robinson who drove a shot wide with his left foot.
With the Blades in the ascendancy, boss Wilder replaced McBurnie with McGoldrick just past the hour mark.
The Blades found plenty of the famed fluency which resulted in the ascension into the Premier League as the natives on the home terraces began to become restless.
On 69 minutes a driving overlapping run from O'Connell was followed by a dangerous cross into the near post which required a vital clearance from Tomori with Robinson lurking.
Soon after Norwood stung the palms of Kepa Arrizabalaga with a long-range strike as United continued to look the more likely to score.
The Blades made another change with just over 10 minutes remaining, as Mousset replaced Freeman.
United continued to surge forward in search of an equaliser with Mousset having an immediate impact with a driving run. After checking inside, he laid the ball to the impressive Stevens whose effort took a deflection which almost wrong-footed Arrizabalaga.
With three minutes remaining Mount went close after Henderson punched a free-kick clear to the midfielder on the edge of the area, but he drilled his effort wide.
At the other end Mousset's cut back almost brought an opportunity for sub Ben Osborn, with the ball eventually breaking to Robinson whose effort was blocked.
With time ticking away though United bagged a thoroughly deserved equaliser. Brilliant work down the left by Robinson ended with a dangerous cross towards the back post, where Zouma touched the ball beyond Arrizabalaga.
Blades: Henderson, Baldock, Stevens, O'Connell, Basham (Osborn 84), Lundstram, L. Freeman (Mousset 79), McBurnie (McGoldrick 63), Robinson, Egan, Norwood.
Unused: Sharp, Stearman, Moore, Bešić.
Chelsea: Kepa, Azpilicueta, Zouma, Tomori, Emerson, Jorginho, Kovacic (Batshuayi 83), Pulisic, Barkley (Willian 60), Mount, Abraham (Gilmour 83).
Unused: Caballero, Christensen, Alonso, Giroud.
As it happened...
United fans in good voice in the away end, as the action gets underway here at the Bridge.
After a quiet opening, O'Connell has to be alert to snuff out the danger as Abraham looked poised to shoot in the box.
United force a corner from Henderson's long free-kick forward.
From Norwood's left-wing delivery, Abraham heads clear at the near post.
The Blades enjoying a fair amount of posession, but despite a heavy touch, Zouma manages to avoid conceding a corner.
Abraham looks offside from Tomori's long ball forward, but drags his effort wide of Henderson's far post anyway.
Goal for Chelsea. Abraham fires home after Henderson spills his first headed attempt under pressure from Pulisic (1-0)
United go looking for a response, but Basham fires over from a promising position after Zouma failed to clear Stevens cross.
On the attack again, O'Connell, Stevens and Robinson fashion an opening for Freeman, who sees a shot blocked for a corner.
George Baldock in the thick of the action
The players grab a quick drink, as Tomori receives treatment following a challenge with McBurnie.
John Lundstram in the Blades engine room at the Bridge
United suffer a major scare as Kovavic breaks into the United area, before dragging his effort wide of the far post.
The Blades almost level, Lundstram frees Basham down the right, but from his low cross, Robinson glances a diving header wide.
Goal for Chelsea. Abraham gets his second of the afternoon, capitilising on a mix-up between Egan and O'Connell. (2-0)
Chelsea move forward and Mount sees an effort deflected behind for a corner. Azpilicueta heads home, but the ball had drifted out of play on it's way into the box.
McBurnie cautioned on the stoke of half-time.
United trial 2-0 at the break, after a brace from Abraham.
No changes from either side at the break, as the second half gets underway here in London.
GOALLLLL! Robinson with his first Premier League goal!
United strike the first blow of the second half as Robinson side foots past Kepa after Stevens surging run down the left.
Attendance at Stamford Bridge - 40,560
Backed by excellent travelling support as always, United push forward looking for an equaliser, with Zouma having to make a tackle to deny McBurnie a chance to shoot
Henderson saves the Blades, denying Abraham a hat-trick with an excellent reflex save, before Lundstram makes a crucial block to block Emerson with the rebound.
At the other end, Robinson gets one on one with Tomori, but drags his effort wide.
The hosts make a change, with Willian replacing Barkley
Boss Wilder makes United's first change with McGoldrick taking the place of McBurnie
The Blades, once again attacking down the left force a corner, from which Lundstram heads straight at Kepa
United once again pile forward in numbers, but Kepa is equal to Norwood's dipping effort from distance.
United's second change, sees Mousset replace Freeman, the Frenchman's Premier League debut for the Blades
Enda Stevens, with the assist for Robinson's goal
Mousset almost has an immediate impact, putting Chelsea on the back foot, before a deflected effort from Stevens almosts wrongfoots Kepa.
Double substitution for the home side, with Batshuayi and Gilmour replacing Abraham and Kovacic
For the Blades, Osborn replaced Basham
Henderson punches clear a Willian free-kick and Mount's follow up goes wide of the post.
At the other end, Mousset breaks clear down the right and the ball lands at the feet of Robinson, who sees his shot blocked at the expense of a corner.
GOALLLLLLLL! The Blades are level here at Stamford Bridge
Robinson curls in a ball from the left and Mousset's presence forces Zouma to deflect the ball home, much to the delight of those packed into the away end. (2-2)
Four minutes of additional time here at Chelsea. (2-2)
United earn a deserved point at Stamford Bridge, showing great character to come from two goals down at the break. Robinson with his first goal for the club.
2-2 it finishes in the capital, with the players heading over to thank the fans for their terrific support at Stamford Bridge.
Boss Chris Wilder enjoys a moment saluting the away end before the players leave the field.
Thanks for your excellent support once again, safe trip home and we'll see you again at the Lane, following the forthcoming international break.