Billy Sharp and Sander Berge scored injury-time goals as Sheffield United ended non-league Wrexham's FA Cup run in a pulsating fourth-round replay.
Anel Ahmedhodzic put United ahead early in the second half before Paul Mullin's penalty brought Wrexham level.
Mullin had a second spot-kick saved by Adam Davies before Sharp scored deep in stoppage time.
Berge scored United's third on the counter to set up a fifth-round tie against Tottenham Hotspur.
The Yorkshire club can look forward to hosting Spurs having finally overcome National League title contenders Wrexham after two exhilarating ties.
United had required John Egan's stoppage-time equaliser to secure a 3-3 draw and a replay in the original tie and they needed late goals once more at Bramall Lane.
Both managers see promotion as their priority this season and with that in mind the hosts made five changes from the original game, including a full debut for Ismaila Coulibaly.
Wrexham's line-up showed seven changes from the team which had won 2-1 at Altrincham in their previous National League game.
The hosts, as expected, dominated the early possession although they did not create any clear-cut chances during the opening 10 minutes, while Wrexham looked to attack on the counter.
A good home move saw Iliman Ndiaye playing in James McAtee but his shot did not trouble goalkeeper Rob Lainton, while an Egan header was cleared by a well-disciplined Wrexham defence.
Sander Berge celebrates after his goal ended any slim hope of a Wrexham comebackMullin, looking to add to his tally of eight goals in this season's competition, tried his luck from the edge of the area with a shot which deflected off Egan.
United responded with a counter-attack and McAtee broke clear, but opted to go alone rather than squaring to Ndiaye and put the ball wastefully wide.
Lainton, who has fought back from a career-threatening wrist injury, made two crucial saves in the space of two minutes to deny Ahmedhodzicć's close-range effort and then Sharp.
Although United looked the more likely of the sides to score, Wrexham comfortably kept them at bay to stay in the game at the break.
Wrexham, now attacking the end housing 4,700 noisy travelling fans, started the second period brightly.
But it was Paul Heckingbttom's team who went ahead with Ben Osborn combining well on the right-hand side with Ahmedhodzic, who smashed the ball past Lainton for his fifth goal of the season.
Heckingbottom's men went in search of a second and Sharp was set up by McAtee only to have his effort brilliantly saved.
That missed opportunity proved significant moments later as Mullin was brought down just inside the area by Ahmedhodzic.
Paul Mullin scored his ninth FA Cup goal of the season to put Wrexham levelMullin stepped up and hammered the penalty straight down the middle for his 29th goal of the season in all competitions.
Wrexham were awarded a second penalty when substitute Oliver Norwood brought down Mullin, but on this occasion the striker was denied by an excellent save by Wales international Davies.
Mullin's involvement soon came to and end due to injury, while during the last few minutes of normal time Sharp went close for the home side before having a goal disallowed for offside.
The game was in stoppage time by the time United felt they should have had a penalty when Norwood's shot was handled.
The referee's decision to wave play on proved academic as a long clearance found Sharp on the left and he coolly slotted past Lainton.
As Wrexham looked for an equaliser that would have taken the game into extra time, they were hit on the counter and Berge scored a third from close range to seal the win and bring the curtain down on Wrexham's cup adventure.
Sheffield United manager Paul Heckingbottom said:
"When it's tense and it's 1-1 we get that breakaway goal and I'm pleased it fell to Bill.
"I've got the utmost respect for them and what they are doing and it's only a matter of time before they achieve their goals.
"But it doesn't mean we were going to let them win for everyone else's fairytales. We've got to be selfish in that respect.
"Credit to my players for the focus and determination to make sure we're not on the wrong end of it."
Wrexham manager Phil Parkinson said:
"What a performance from the lads. We were the better team I thought in the second half.
"I didn't doubt that we'd respond, I felt we would and we did. We got the penalty to get us back in it and I felt that we were the team that was going to win the game.
"But the second penalty is obviously the key moment in the game. Cruelly we've lost it late but we've taken a Premiership-bound team in two games right to the wire and that's enormous credit to our lads.
"The resilience of the side was outstanding."
Line-ups
Sheff Utd
Formation 3-5-2
1Davies
15Ahmedhodzic12Egan19Robinson
6Basham17Coulibaly8Berge28McAtee23Osborn
29Ndiaye10Sharp
1Davies15AhmedhodzicSubstituted forLoweat 78'minutes12EganBooked at 75mins19Robinson6Basham17CoulibalyBooked at 45minsSubstituted forNorwoodat 68'minutes8BergeBooked at 90mins28McAteeSubstituted forBrooksat 90+8'minutes23Osborn29Ndiaye10SharpSubstitutes
13Lowe16Norwood18Foderingham26Clark30Arblaster35Brooks39Starbuck41MarshWrexham
Formation 5-3-2
1Lainton
14Forde32Cleworth4Tozer26Lennon19Mendy
30Jones8Young20Cannon
10Mullin18Dalby
1Lainton14Forde32Cleworth4Tozer26LennonSubstituted forO'Connorat 74'minutes19MendySubstituted forMcAlindenat 60'minutes30Jones8Young20CannonSubstituted forLeeat 82'minutes10MullinSubstituted forBickerstaffat 82'minutes18DalbySubstituted forPalmerat 60'minutesSubstitutes
9Palmer11McAlinden17Hosannah22O'Connor24Butler27Bickerstaff31Watson34James38LeeReferee:Leigh DoughtyAttendance:20,310Live Text
Match ends, Sheffield United 3, Wrexham 1.
Second Half ends, Sheffield United 3, Wrexham 1.
Delay over. They are ready to continue.
Substitution, Sheffield United. Andre Brooks replaces James McAtee because of an injury.
Delay in match because of an injury James McAtee (Sheffield United).
Goal! Sheffield United 3, Wrexham 1. Sander Berge (Sheffield United) right footed shot from the centre of the box to the top left corner. Assisted by James McAtee with a through ball.
Goal! Sheffield United 2, Wrexham 1. Billy Sharp (Sheffield United) right footed shot from the centre of the box to the bottom right corner following a fast break.
Attempt blocked. Ollie Palmer (Wrexham) right footed shot from outside the box is blocked. Assisted by Jake Bickerstaff.
Sander Berge (Sheffield United) is shown the yellow card for a bad foul.
Foul by Sander Berge (Sheffield United).
Elliot Lee (Wrexham) wins a free kick in the defensive half.
Attempt blocked. Ben Osborn (Sheffield United) right footed shot from outside the box is blocked. Assisted by James McAtee.
Attempt missed. John Egan (Sheffield United) header from the centre of the box misses to the right following a corner.
Corner, Sheffield United. Conceded by Elliot Lee.
Attempt blocked. Oliver Norwood (Sheffield United) right footed shot from outside the box is blocked. Assisted by Iliman Ndiaye.
Attempt missed. Max Lowe (Sheffield United) header from very close range is high and wide to the left. Assisted by John Egan with a headed pass following a corner.
Corner, Sheffield United. Conceded by Elliot Lee.
Attempt blocked. Oliver Norwood (Sheffield United) right footed shot from outside the box is blocked. Assisted by Sander Berge.
Offside, Sheffield United. Oliver Norwood tries a through ball, but Billy Sharp is caught offside.
Attempt missed. Billy Sharp (Sheffield United) right footed shot from the centre of the box is too high. Assisted by Oliver Norwood with a through ball.
