The game was largely dire, with United defending stoutly throughout and sitting very deep for the majority of the 120 minutes, but a goal in the dying seconds sealed the win.
Fulham had more of the ball in the first half, but it was the League One side that had the better chances. The first came in the opening few minutes, when Jamie Murphy picked the ball up just outside the area and shot, causing Fulham keeper David Stockdale to scramble across his goal, but it went just wide of the post.
Later on in the half, on-loan full-back John Brayford did well to win the ball on the right, but after advancing towards the box, his shot skewed just wide of Stockdale's post.
The second-half continued in much the same manner, with United defending deep but the hosts lacking the imagination to break down their staunch defence. Again, Sheffield United had the better of the chances, while Fulham had to wait until the 89th minute for their first effort on target.
Sheffield United will now play either Preston or Nottingham Forest in the fifth round, who have their own fourth round replay on Wednesday night.
120 - GOAL! SHEFFIELD UNITED STEAL IT! A corner comes over, Maguire rises at the far post and heads it back across goal, and sub Shaun Miller nods it into the corner of the net. Praise be.
Fulham's first shot on target in the second half came in the 89th minute.
They only had two shots on target in the whole 120 minutes. Sheffield United had three.
Fulham had a whopping 68% possession.
Fulham are in some serious trouble - This isn't news, given their position at the bottom of the table and their recent form, but if they required proof it was their inability to break down a struggling League One team. Sheffield United are second-bottom of the table and lost to Crewe at the weekend, and although they defended well and in numbers, Fulham should really have been able to do more than they did.
MAN OF THE MATCH
John Brayford - Something of a back-handed compliment in a game as bad as this, but the on-loan full-back provided plenty of drive from the right, and it was his run that lead to the corner from which United scored.
FULHAM: Stockdale 5, Passley 5, Hangeland 5, Burn 5, Amorebieta 4, Kasami 3, Tanković 4, Parker 4, Kačaniklić 4, Dempsey 4, Rodallega 3. SUBS: Sidwell 5, Duff 5, Dejagah 6.
SHEFFIELD UNITED: Howard 6, Brayford 7, Maguire 7, Collins 6, Harris 6, Flynn 6, Coady 6, McGinn 6, Scougall 5; Porter 6, Murphy 6. SUBS: Hill 5, Baxter 5, Miller 6.
THE MATCH IN A TWEET