Chris Wilder’s side remain on the brink of a record points low come the end of season as Palace ended a five-game Premier League losing streak.
The hosts were clearly the sharper of the two sides early on as Roy Hodgson’s hosts deservedly edged in front on five minutes.
Christian Benteke’s deflected shot ricocheted around the United box and Jeff Schlupp coolly waited for his chance to tuck past Aaron Ramsdale.
That goal failed to spark either side into life before the break with substitute Eberechi Eze waiting until first half added time to make it 2-0.
The former QPR star has enjoyed an eye-catching start at Palace and he dipped in and out of Blades tackles from halfway before bending home past Ramsdale.
Wilder threw on Lys Mousset and Rhian Brewster for the final half hour to inject some urgency into things, but they could do nothing as the Blades took another step inevitable step closer to the drop.
Full Time at Selhurst Park it’s Crystal Palace 2 Sheffield United 0