Rodallega's low shot spared more misery for Fulham this season, with the London club that is just one point above the relegation zone in the Premier League standings narrowly averting an early exit against their 10-man opponents.
Chris Porter put the hosts ahead in the 31st minute as he diverted a shot past David Stockdale. But the League One club had Michael Doyle sent off for a kick at Muamer Tankovic early in the second half and could not hold its lead.
Sheffield United manager Nigel Clough praised his players for their grit but said the referee's decision to send off his player was a bit harsh.
"There was some sort of contact, whether it was enough to warrant a red card I'm not sure," he said.
Fulham manager Rene Meulensteen, whose priority is to keep his team in the Premier League next season, made 11 changes for the tie against a side that knocked out Aston Villa in the previous round but is facing a tough relegation battle in its division.
On a waterlogged pitch, Sheffield United looked like it could hold on even after Doyle's sending off, and even threatened to extend its lead when Ryan Flynn led a swift counterattack down the right only to see his low shot stopped by Stockdale.
Both sides were denied penalties as Rodallega and Flynn appeared to be fouled in the area.
Meulensteen admitted his side lacked the quality to prevail but was happy with his youngsters' performance.
"They gave it their all and got their noses in front," Meulensteen said. "If there's any positives to take from the game there's two things. Obviously we're still in it, that's one, but the young boys we brought in did excellent."
FA Cup: Fulham forced to replay by Sheffield United
Advertisement