Two stoppage time goals from Billy Sharp and Sander Berge edged out the Red Dragons in what was yet another barnstorming Emirates FA Cup clash.
It took 50 minutes for the Blades to break through the resilient Wrexham defence, as Anel Ahmedhodzic fired the ball past Lainton from close range.
Paul Mullin found the leveller from the spot just before the hour mark, with an excellent strike leaving Adam Davies no chance of saving.
However, in the 71st minute Mullin had another chance from a penalty kick, but this time Davies guessed correctly denying Wrexham of the lead.
At the death the high-flying Championship side capitalised on their pressure, and two stoppage time goals from Billy Sharp and Sander Berge secured victory.
Phil Parkinson named seven changes to the team that ran out victorious at Altrincham last weekend.
Rob Lainton returned in goal; Anthony Forde, Harry Lennon and Jacob Mendy came into the defence, James Jones and Andy Cannon back in the midfield, and Sam Dalby partnering Paul Mullin.
Paul Heckingbottom rang the changes too, making five changes from their goalless draw on Saturday against fellow Yorkshire side Rotherham.
It was the hosts who looked to make use of home advantage, and John Egan found himself rising at the back post just like the first fixture, but Lainton made a comfortable save.
The hosts put the Red Dragons under pressure with a barrage of corners from both sides, but the defence stood firm.
On the half hour mark the hosts missed a golden opportunity to take the lead, James McAtee capitalised on Mendy’s missed interception, racing through on goal but fired wide of Lainton.
Chances were hard to come by for the Red Dragons in the opening period, but any relief came through the left-hand side and the burst of pace from Jacob Mendy.
The Blades pressure continued to mount, but once again Wrexham stood firm, and it was Lainton who came to the rescue, making a superb save from Ahmedhodzic’s strike.
After Wrexham withstood their pressure in the first period, the hosts looked to make it count again in the second half, and Ahmedhodzic got his goal, sliding past Lainton after a smart move.
However, it wasn’t all one-way traffic, as the Red Dragons were roared on by the travelling faithful and got back into the game.
Mullin broke into space inside the area, and was hauled down earning a penalty, and he lashed it home sending the away end into raptures.
Parkinson’s side got into their groove and began to probe the Blades' backline and Ben Tozer’s throws continued to cause problems.
Ten minutes after levelling Mullin had another opportunity to score from the spot and take the lead, but this time Davies guessed right, making a strong save.
After Wrexham’s strong pressure, the pendulum began to swing back in the Blades' favour, forcing Lainton to make another series of saves.
Just as the contest looked as though it was heading to extra time, the hosts had the ball in the net in the 88th minute, as Sharp converted, but he was judged offside.
However, in added time the resilient Wrexham defence was breached, as Max Cleworth couldn’t claim the ball, and Sharp this time ran through and took the lead.
Wrexham pressed for an equaliser and battled away, but Berge lead a counter attack, and made it three, two minutes from time sealing the victory.
Sheffield United: Davies, Ahmedhodzic (Lowe 77’), Egan, Robinson, Basham, Coulibaly (Norwood 67’), Berge, McAtee (Brooks 98’), Osborn, Ndiaye, Sharp
Subs not used: Foderingham, Arblaster, Clark, Marsh and Starbuck
Wrexham: Lainton, Forde, Cleworth, Tozer, Lennon (O’Connor 74’), Mendy (McAlinden 60’), Young ©, Jones, Cannon (Lee 81’), Mullin (Bickerstaff 81’), Dalby (Palmer 60’)
Subs not used: Watson, James, Butler and Hosannah,
Attendance: 20,310