A brave effort from 10-man United ended in defeat as Ezri Konsa's second-half header secured a 1-0 success for Aston Villa.
The Blades played 78 minutes a man light after John Egan's red card on 12 minutes, but a gutsy display ensured the hosts had to work exceptionally hard for the points which were claimed by Konsa's close range header.
Even with 10-men United could have been in front as Chris Basham was felled in the area but John Lundstram's penalty was saved by Villa stopper Emi Martinez.
Boss Chris Wilder handed striker Oli Burke a first United Premier League start as he made three changes to the side which opened the league season against Wolves.
Burke started in attack alongside David McGoldrick, both retained from the Carabao Cup tie against Burnley, with Billy Sharp and Oli McBurnie on the bench.
Sander Berge was selected in midfield for Ollie Norwood, whilst Egan took the captain's armband.
Villa started brightly with John McGinn flashing Matty Cash's deep cross over after just two minutes, whilst at the other end Konsa made a vital clearance from a low cross as McGoldrick waited to pounce.
Lundstram found himself in the book on 10 minutes for a late lunge on Jack Grealish but worse was to follow two minutes later. A long punt froward from Tyrone Mings had Ollie Watkins interested and in the ensuing tussle with Egan, the Irishman was adjudged to have denied a goalscoring opportunity and was given his marching orders.
With the extra man, Villa put United under pressure, but the Blades successfully defended a series of dangerous corners from Conor Hourihane as Aaron Ramsdale was well protected.
On 22 minutes a corner was worked to the edge of the area where Matt Targett played it to the left before it was eventually sent into the mix, but Douglas Luiz's weak header landed into the grasp of Ramsdale.
On 30 minutes Jack O'Connell made a goal saving clearance under pressure inside the six-yard box as a low cross from Targett threatened the United goal.
McGoldrick was sacrificed for Ethan Ampadu as United readjusted following the red card and soon after came another big talking point. United produced a swift counter attack when Lundstram freed Burke down the left, he sprinted towards goal before cutting in from the left, sending Basham clear. As he was about to shoot, he was clipped by Targett for a clear penalty with the offender seeing yellow. Lundstram stepped forward but his effort from 12 yards was clawed away by Martinez diving to his right.
Villa not surprisingly dominated possession but United looked comfortable during the first 15 minutes of the second half as the hosts failed to test Ramsdale.
The Blades carried a threat on the counter and Berge almost found an opportunity after initially latching onto a pass into the area, but he couldn't get the ball out of his feet in time under pressure to fire an attempt on goal.
On 63 minutes Villa netted what would prove to be the winner. A corner on the far side was flicked on by Mings and KONSA arrived with a well-placed header which nestled into the bottom corner.
The Blades reacted by bringing on Ben Osborn for John Fleck, whilst McBurnie also replaced Basham as Wilder went for broke.
Villa created numerous half chances but a stoic United kept them largely to arm's length whilst pushing at the other end when Ampadu's snapshot arrowed wide.
Inside the final 15 minutes Watkins, Grealish and Trézéguet went close for Villa but United remained a threat as Berge had a goalbound effort blocked.
With a minute to go a corner from Osborn was flicked on by McBurnie but Berge on the spin put an effort wide from a tight angle.
United continued knocking right to the end but Villa saw the game out despite a terrific effort from Wilder's Blades.
Aston Villa: Martínez, Cash, Konsa, Mings, Targett, Douglas Luiz, Hourihane (Davis 62'), Trézéguet, Watkins, Grealish.
Unused: Steer, Elmohamady, Hause, Taylor, Nakamba, El Ghazi.
Blades: Ramsdale, Baldock, Stevens, Fleck (Osborn 64'), O'Connell, Basham (McBurnie 68'), Lundstram, Berge, Egan, Burke, McGoldrick (Ampadu 31').
Unused: Sharp, Norwood, Foderingham, Robinson.
As it happened...
David McGoldrick over the ball and United get this match underway.
First attack for Villa and it's a half-chance as Matty Cash gallops forward into space down the right. He sends in a deep cross which John McGinn fancies at the far post, but it is a tight angle and at full stretch he guides the ball over.
Another dangerous cross, this time by Douglas Luiz. McGinn gets a touch on it and Basham clears over his own bar.
Hourihane delivers the corner which is glanced wide by Tyrone Mings.
United free-kick midway through Villa territory.
Lundstram sends in a cross but it fails to beat the first man and Villa clear.
United get another chance to deliver and Konsa makes crcuial interception with McGoldrick waiting.
Lundstram is the first into the book after a challenge which takes out Jack Grealish.
Appeals as Matt Targett goes down in United's area, waved away.
Red card for Egan!
The skipper is sent off after a Mings' ball over the top sees the Irishman put hands on Ollie Watkins who was trying to break clear. VAR check.
Decision stands. Denial of goalscoring opportunity says the team at Stockley Park. United down to 10 men.
United win a free-kick on the right, delivered by Lundstram and headed behind by Hourihane.
The resulting corner is headed clear by Mings and Baldock's return cross is caught by Martinez.
Villa free-kick now and a wicked delivery from Hourihane is headed behind by Lundstram, Berge bravely heads the following corner clear.
Another free-kick and another devilish cross from Hourihane, flicked clear by O'Connell. McGoldrick then clears the corner. United under pressure.
Watkins heads against a defender to win another corner as Fleck fails to clear.
Hourihane again with the cross which is narrowly missed by Mings attacking the near post.
Yet another corner as Stevens blocks a cross from the right.
This one goes to the edge of the area. Targett lifts it left and then it goes in but Luiz heads straight at Ramsdale.
United have gone 4-4-1 by the looks of things with McGoldrick going to the left side and Lundstram to the right.
Back-to-back short corners for Villa defended by United as Cash has a shot from 20 yards blocked.
Fantastic clearance by O'Connell as Grealish dances into the area before finding Targett whose low cross needed defending.
Substitution for United as Ethan Ampadu is handed his Blades Premier League debut, replacing David McGoldrick.
Basham into right midfield, Ampadu partners O'Connell and Fleck goes out to the left at first glance.
Penalty to United!
A counter attack sees Lundstram sprint clear before feeding Burke. He sends Basham through on goal and he's tripped by Targett. Penalty! Only a yellow though for Targett.
After a VAR check, the peanlty is awarded...
Lundstram's penalty is clawed away by Martinez who dives to his right.
Villa back into their stride and Ampadu's first contribution is to head clear under pressure.
Hourihane then sends a shot over from 20 yards.
Grealish into the area and his low cross wins a corner, Basham then clears under pressure and the referee agrees he's fouled and United have a free-kick.
Four minutes added time.
Just before the break Hourihane with another dangerous centre which is fired over from a tight angle.
Aston Villa 0 - 0 Blades
Incident packed half where John Egan has been sent off and John Lundstram has seen a penalty saved.
Villa get the second half underway!
A couple of early forays seen off by United. 0-0.
Ramsdale quickly out to make a brave claim at the near post from Targett's cross. He gets a knock too, but he's okay to continue.
Trézéguet whips in a cross from the right but the header is harmlessly over as United continue to work hard out of possession.
United make a mark on Villa with a nice counter. A low pass almost has Berge in on goal but he can't quite get it out of his feet under pressure.
Nice play by Stevens who takes on a couple of Claret shirts before lifting a ball over the top for Burke to chase. Just too strong though as Martinez claims just inside his area.
Keinan Davis replaces Hourihane for Villa.
Villa strike as a corner is headed on by Mings and Konsa's header is well placed into the bottom corner.
United make a change as Fleck is replaced by Ben Osborn.
United respond as Stevens' centre is headed behind by Konsa.
Lundstram's corner is right into the mix but Mings heads clear.
Close for Villa as Grealish buys half a yard on the edge of the area but the low shot is just wide.
Final change for United as Basham makes way for Oli McBurnie.
United win a free-kick 35 yards from goal.
Osborn delivers, McBurnie flicks on, Villa only half clear allowing Ampadu a snapshot from 20 yards which goes wide. Decent effort.
United starting to push bodies forward now, so they are a little stretched at the other end as Trézéguet sends a low cross right through the six-yard area.
Grealish dinks a cross to the back post but Trézéguet drags an effort well wide.
Watkins with a curling effort from the angle which is narrowly wide of the post.
United dangerous on the counter.
A swift move involving Osborn and McBurnie ends with Burke pulling a cross back which almost found McBurnie.
Then Berge runs into the area before seeing a shot blocked.
Chance to win it forn Villa but Grealish drags a shot wide of the near post.
Cash booked for time wasting on a throw in.
McGinn booked as he stops Lundstram on the counter.
Trézéguet pulls the ball back from the right for McGinn to shoot but he drags his effort wide from 20 yards.
Ramsdale palms a low cross to safety and at the other end United work themselves into a crossing position but Lundstram's centre is too close to Martinez.
Late corner for United won down the right.
Osborn delivers, McBurnie flicks on but Berge on the spin sends a difficult chance wide.
Three added minutes.
Ampadu loses the ball, Villa counter but Lundstram gets back to block a Grealish effort which would have won it for sure.
Villa keeping the ball near the quadrant from the corner.
Aston Villa 1 - 0 Blades
Fantastic effort from 10-man Blades but Konsa's second half effort wins it for Villa.