After James McAtee somehow missed a gilt-edged one-on-one chance to break the deadlock in the first half, the Blades struck first through Anel Ahmedhodzic on the 50-minute mark.
However, Wrexham talisman Paul Mullin crashed home a penalty nine minutes later to restore parity, but the 28-year-old then had another spot kick saved by Adam Davies before coming off with an apparent hamstring injury.
The National League side only needed to survive six minutes of stoppage time to force an extra half-hour, but two late Blades counter-attacks ended with Billy Sharp slotting home and Sander Berge hammering the ball into the roof of the net.
Sheffield United can now prepare for a home tie against Tottenham Hotspur in round five, but a giant killing did occur at Grimsby Town's Blundell Park, as the League Two side swept aside Championship counterparts Luton Town in a dominant 3-0 success.
A sensational first half for the hosts saw Harry Clifton, Danilo Orsi-Dadomo and Daniel Amos all find the back of the net, and a shell-shocked Luton had no answer in the second 45 minutes.
Grimsby have been rewarded for their efforts with a trip to Premier League strugglers Southampton in round five, while Fleetwood Town edged the all-League One battle against Sheffield Wednesday.
A solitary strike from Carlos Mendes Gomes on the hour mark was all it took to sent Fleetwood through to the last 16, where Burnley now await them following the Clarets' own dramatic late win versus Ipswich Town.
Within the first three minutes of the contest, Nathan Tella had given Burnley the lead before George Hirst immediately levelled for the Tractor Boys, who - like Wrexham - were mere minutes away from forcing extra-time.
However, Tella's second of the match in the fourth minute of second-half injury time sent Vincent Kompany's men through to round five.