United made it back-to-back victories and stretched a Premier League unbeaten run to four games after a convincing 3-0 success against high-flying Chelsea.
Inspired by a late win over Wolves on Wednesday night, United carried momentum into the contest and were good value for the three points after a David McGoldrick brace either side of a well-taken header from Oli McBurnie.
The win moves the Blades into sixth with just three Premier League games remaining.
Manager Chris Wilder made one change to the side which beat Wolves in dramatic fashion on Wednesday night.
The Blades boss opted to recall striker McGoldrick, who was fit-again after a recent foot injury, with Billy Sharp dropping to the bench.
United came flying out of the blocks and put the visitors on the back foot from the off after winning an early corner, shortly afterwards George Baldock crashed into Christian Pulisic with a strong challenge and received a yellow card after just three minutes.
The Blades maintained their high tempo start and on five minutes Ollie Norwood's corner was only clawed away as far as Ben Osborn by Arrizabalaga, but the former Nottingham Forest midfielder blazed an effort well over.
At the other end, Chelsea threatened for the first time when Ross Barkley sailed in a dangerous centre which was headed wide by Pulisic under pressure from Baldock.
The positive start for United was rewarded with the opening goal on 18 minutes. After good interplay between McBurnie and Osborn almost created an opening, the Blades kept the attack alive by working it wide to Baldock. The wing-back stood up a perfect cross for McBurnie at the back post who struck the ball first time. His effort took a slight deflection off a Chelsea body which caught out Arrizabalaga who could only parry to McGOLDRICK who was on hand to convert from close range.
Chelsea enjoyed a spell of possession but there was no way through a solid United who pressed their opponents throughout.
With nothing coming from the visitors, it was United who looked more likely to score and it was no surprise when the Blades added a second. Enda Stevens worked himself into an excellent position down the left after a sublime one-two with Osborn. The Irishman then stood up a perfect cross for an unmarked McBURNIE to powerfully head beyond the stranded Arrizabalaga.
It took 43 minutes for Chelsea to work Dean Henderson for the first time when from almost nothing Reece James drilled in a powerful effort from 20 yards which the United 'keeper parried clear with both hands.
Chelsea upped the tempo at the start of the second-half, but despite an increased energy, the Blades rarely looked threatened by the Londoners.
If anything it was United who looked more of a threat and when Chris Basham surged forward down the right his cross caused problems for James who had to put the ball over his own bar with Osborn ready to pounce.
Chelsea mustered nothing in terms of clear-cut chances with sub Marcos Alonso heading well wide and Ross Barkley crashing a free-kick into the United wall.
After the introduction of Olivier Giroud, he almost created a chance out of nothing with his first touch as he struck a first time shot from a long punt upfield just wide of the near post.
Inside the final 20 minutes, John Egan almost made it three in three games when he was close to converting Osborn's low centre, whilst at the other end Jack O'Connell made a telling block to deflect a Cesar Azpilicueta effort wide.
With 13 minutes remaining United sealed the points with a third. McGOLDRICK started the move with a run from deep before laying a pass into the channel for Mousset to chase. His low cross into the area was controlled by Antonio Rudiger straight into the path of McGoldrick who lashed the ball beyond Arrizabalaga for his second.
United should have had a fourth before the end when McGoldrick picked the pocket of Jorginho before releasing Mousset but when clear on goal he dinked his effort just wide of the post.
United comfortably saw out the remaining minutes to record yet another clean sheet and a valuable three points.
Blades: Henderson, Baldock, Stevens, O'Connell, Basham (Jagielka 68'), McBurnie (Mousset 63'), Egan, Norwood, McGoldrick, Osborn, Berge (Lundstram 63').
Unused: Sharp, K. Freeman, Robinson, Moore, Rodwell, Živković.
Chelsea: Kepa, James (Hudson-Odoi 75'), Christensen (Rüdiger HT), Zouma, Azpilicueta, Mount (Alonso HT), Jorginho, Barkley (Loftus-Cheek 78'), Pulisic (Giroud 65'), Abraham, Willian.
Unused: Caballero, Kovacic, Batshuayi, Bate.
As it happened...
Blades get this one underway.
Positive start from United who win a corner in the first minute.
Norwood's centre is good, but Kepa is adjudged to have been fouled. Free-kick to Chelsea.
First yellow already.
George Baldock crashes into Pulisic and he's cautioned.
Patient build-up from United and Norwood swings in another great cross.
McGoldrick attacks the ball, the final touch is off a Chelsea jersey. Corner.
Norwood's corner is clawed away by Kepa. Osborn sees a chance and steams onto the loose ball but crashes an effort over the bar.
First threat from Chelsea.
Barkley with a lovely cross into a good area. Pulisic attacks it, but heads wide under pressure from Baldock.
Chelsea have Andreas Christensen down after an awkward fall. Break in play.
Christensen fully recovered, the game is back underway.
United will be pleased with the start.
First real evidence there of Chelsea settling into their stride.
A long spell of possession is ended with a poor cross from the left, but the visitors have started to settle a little now.
United have the lead. First Premier League goal of the season for David McGoldrick.
Cross from Baldock finds McBurnie who hits it first time. It takes a deflection, but Kepa gets a hand to it but McGoldrick on hand to convert.
United have been excellent, Chelsea yet to have an effort on goal.
Good again from United.
Chelsea enjoying a lot of the ball but United have bodies back and are pressing their opponents at every opportunity. Dean Henderson well protected so far.
That's a second for United.
Lovely one-two between Stevens and Osborn. The former stands up a terrific cross and McBurnie - unmarked - powers his header home.
Chelsea close to a counter there as Abraham chases a long ball before linking up with Pulisic.
United get back in numbers though and snuff out the danger.
Chance for Chelsea and it came from nothing.
Nothing really on so Reece James drills in a low shot from the edge of the area and Henderson forced to parry with both hands.
Two added minutes.
Blades 2 - 0 Chelsea
Brilliant first-half from United who lead through goals from McGoldrick and McBurnie.
Chelsea making changes.
Rudiger and Alonso replace Christensen and Mount.
We're back underway,
Half chance for Chelsea. Deep cross to the back post from the right and Alonso heads harmlessly wide.
Swift counter attacking play from United as McGoldrick frees Basham who whips in a first-time cross looking for Osborn. James forced to clear over his own bar and Chelsea clear the resulting corner.
Chelsea have quickened the pace in the last five minutes but United are looking good. Still nothing of note created from the visitors.
Change of tempo again by Chelsea. Pulisic wins a corner after a quick counter.
In comes the cross and McBurnie is the dominant player to head clear.
Good spell by Chelsea this but nothing at the end of it so far.
Willian's cross this time defended by United who are standing firm.
Clumsy foul by Berge gives Barkley a chance to shoot with a free-kick but he drills it straight into the wall.
United's first changes. John Lundstram and Lys Mousset on for Berge and McBurnie.
Abraham and Barkley combine to create a chance for Pulisic but it looks as though Egan is across to make a great block.
Chelsea change as Olivier Giroud replaces Pulisic.
Route one form Chelsea.
Long punt forward and Giroud hits it first time but wide of the near post.
Chris Basham picked up a knock earlier, maybe that's why he's coming off here to be replaced by Phil Jagielka.
Dangerous low cross from Osborn. Egan almost there, the ball squirms loose and Kepa pounces in the nick of time.
Brilliant block from O'Connell as he gets a deflection onto a Azpilicueta shot.
The corner is flicked off Rudiger and Abraham can't divert it towards goal.
Callum Hudson-Odoi next to come on. He replaces Reece James.
A third for United and a second for McGoldrick.
He starts the attack with a run from deep, he finds Mousset on the overlap who drives a low cross into the area. Rudiger then gifts the ball to MGoldrick who fires home.
Loftus-Cheek replaces Barkley.
Giroud header comfortably held. First save Henderson has had to make second half.
That should have been four!
McGoldrick out-muscled Jorginho and played Mousset through on goal but his dinked finish drifts just wide of the post.
Three added minutes as Stevens drills an effort over going for a fourth.
Blades 3 - 0 Chelsea
Wonderful display by United as goals from McGoldrick (2) and McBurnie seal another three points.