Ben Watson's last-minute penalty gave Palace victory and handed under-fire boss Peter Taylor a lifeline.
The Blades took the lead after 48 minutes when Palace's Mark Hudson slammed the ball into his own net.
Palace were level on the hour, Tom Soares finishing off fine work by Dougie Freedman and Carl Fletcher's deflected effort put them ahead.
James Beattie's brilliant lob put United on terms before Watson scored after Chris Morgan fouled Fletcher.
Crystal Palace boss Peter Taylor:
"The rumours make me even more determined. I want to be here.
"The players have tried as hard as they can, and that is all you can ask of
"We deserved something from today's game - just as we have in recent matches, where we haven't managed to win."
Sheffield United manager Bryan Robson:
"I am angry. We spoke in the week about keeping possession better
and about not giving away ridiculous goals - we did exactly the opposite.
"After scoring the goal, we needed to be more calculated in possession, and to take the sting out of the game, but we weren't good enough to do that.
"Conceding 12 goals in seven games is a poor record."
Crystal Palace: Speroni, Butterfield, Hudson, Cort, Craig, Soares, Fletcher, Watson, Green (Freedman 55), Scowcroft (Idrizaj 86), Dickov (Hughes 83).
Subs Not Used: Flinders, Lawrence.
Goals: Soares 60, Fletcher 70, Watson 89 pen.
Sheff Utd: Kenny, Bromby (Webber 80), Morgan, Cahill, Naysmith, Gillespie (Stephen Quinn 74), Montgomery, Tonge, Armstrong, Beattie, Stead.
Subs Not Used: Alan Quinn, Lucketti, Sharp.
Goals: Hudson 48 og, Beattie 76.
Ref: Kevin Friend (Leicestershire).