Former Eagle Neil Shipperley's 55th minute header proved to be the winner but only after referee Ian Williamson had consulted his assistant. Replays seemed to indicate their decision was wrong.
Phil Jagielka continued his impressive recent form, scoring United's opener on 14 minutes from close range after good work in the penalty area by Steven Kabba.
It was unfortunate for Palace as Dougie Freedman had hit the post just 60 seconds earlier.
Tom Soares then almost equalised with a free header within a minute of the Blades' opener.
However, they were level in the final minute of the first half. United skipper Chris Morgan failed to cut out Emmerson Boyce's long clearance, Clinton Morrison fed Marco Reich whose cross was powerfully headed home by Michael Hughes.
Unfortunately, Palace went to sleep from the kick-off allowing Kabba to feed Jagielka whose pass found the unmarked Paul Ifill who slotted home from 12 yards.
Shortly after the restart Ben Watson's curling free-kick was tipped over by United keeper Paddy Kenny and Freedman teed up Hughes but again Kenny saved.
When Kenny was beaten shortly after, from a corner, Morgan cleared the ball off the line.
Boyce's powerful shot was also saved and then came Shipperley's headed goal from Keith Gillespie's left-wing free-kick to make it 3-1 to the visitors.
Freedman responded with a superb run and shot which Kenny saved. Kabba could have wrapped it up soon after when Boyce's mistake allowed him a clear run at goal. However, he went to ground as he rounded Gabor Kiraly. The referee deemed he had dived and showed him a yellow card.
Palace were given late hope when Freedman sent Kenny the wrong way from the penalty spot, after David Unsworth's foul on Boyce, but despite some late pressure they failed to summon an equaliser that they just about deserved.