Shaun Miller sent the Blades through to the next stage of the prestigious cup competition by netting in the final minute of extra-time at Craven Cottage.
The two clubs drew 1-1 in the initial fixture on January 26 at Bramall Lane but Nigel Clough's men this time got the better of Rene Meulensteen's Premier League strugglers.
Miller climbed off the bench in the 97th minute, after regular time had ended 0-0, and provided the killer blow when former Everton youngster Jose Baxter's cross was nodded into his path by Harry Maguire for him to glance home in the 120th minute.
The Blades will now take on the winner of Wednesday night's replay between Preston North End and Nottingham Forest at Bramall Lane on February 15 as Fulham look to focus on their Premier League survival.
2013/14 FA Cup fourth round replay
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