United, who have a habit of coming unstuck against the league's top teams after losing to Reading, Wolves and Burnley at Bramall Lane already this season, forced the early pace against a Palace side that were on a high after recording five victories from their last six games.
In the opening stages, Stephen Quinn's penetrating cross from the right found striker Danny Webber whose glancing header was hacked clear by full-back Nathaniel Clyne as he guarded the far post.
Webber was a fraction away from connecting with Chris Morgan's header as keeper Julian Speroni was forced to tidy up after the Palace defence had dithered.
The London side almost found a way through when they hit United on the break, midfielder John Oster cutting inside from the right flank to lash a fierce 16-yard right-foot strike wide of the target.
United broke the deadlock four minutes before the break after Portuguese centre-back Jose Fonte had blundered as he casually tried to head the ball back to his keeper.
The ball ballooned into the air as Nathan Dyer, on loan from Southampton, ran in to coolly beat Speroni with a low strike from 18 yards.
Palace almost levelled matters a minute later, midfielder Carle hitting a left-foot shot on the run that was pushed around the post in acrobatic fashion by Paddy Kenny.
Palace were back on level terms in the 48th minute and it was the Blades' centre-back Morgan who was at fault. The United skipper failed to clear Oster's corner from the right as he allowed Palace defender Paddy McCarthy to finish from eight yards out.
Speroni pulled off a stunning save in the 65th minute as United stepped up the pace, diving to his left to snatch Webber's glancing header from Quinn's free-kick.
Kenny, not to be outdone, conjured up a save of equal measure tipping a Shaun Derry strike onto the bar before McCarthy hammered the loose ball high over the top.
Beattie scored from the spot after McCarthy had hauled back the United striker in the area as the pair challenged for a Quinn corner. The former Southampton and Everton star clinically slotted home the penalty to register his 11th goal of the season.
However, Carle had the final word hammering in a right-foot strike from just inside the area after Morgan's clearance had fallen at the midfielder's feet.