After a goalless scrappy first-half with both sides missing useful chances, the second half exploded into action with Bryan Robson's side going in front on 48 minutes.
Keith Gillespie's in-swinging corner from the left caught Palace defender Mark Hudson off balance and his sliced clearance sailed past the rooted Julian Speroni.
However, Dougie Freedman was immediately sent on as substitute and the game dramatically changed course.
On 60 minutes a spectacular passing move involving five players ended with Freedman jinking his way into the box before squaring the ball to Tom Soares who blasted into the roof of the net from ten yards out.
Nine minutes later Palace were in front. Freedman was in the action again with a clever flick to Tony Craig.
The Palace full-back crossed from the byline and, although it took a deflection off a Sheffield United defender, the ball dropped nicely to Carl Fletcher who drove home from five yards out.
Palace were playing well enough as they sought to increase their lead, but the Blades stung the home crowd as James Beattie latched on to a Leigh Bromby pass and, with the Palace defence wide open, the ex-Everton striker perfectly chipped the ball past Speroni from 15 yards out.
But Palace kept plugging away and one minute from time United were unable to clear and skipper Chris Morgan was adjudged to have held down Soares and the referee pointed straight to the penalty spot.
Up stepped Ben Watson, who capped a fine performance by rifling the penalty past Paddy Kenny's outstretched right hand to give Palace their first win since the opening game of the season.