A Jerome Binnom-Williams header 15 minutes from time was enough to clinch the under-21's first victory of the season at the second attempt.
The left-back put the Blades to the sword when he steered home Jerome Thomas' corner which proved to be enough for Gary Issott's men to collect the victory at Selhurst Park.
The first-half was an evenly-contested affair in terms of possession but there was little in terms of goalmouth action during the opening half-hour. Otis Khan forced Lewis Price to push a testing effort past the post eight minutes in, and Jake Gray almost found a way around Blades keeper George Willis but he managed to push the ball out of the winger's stride.
Palace's best play came though Gray and he nearly found his way onto the scoresheet midway through the first half. Some neat link-up play with Kyle de Silva gave the teenager a chance, but his attempted chip over Willis had too much power and sailed over the crossbar.
Skipper Connor Dymond had a goal chalked off when trialist Rodrigue Ndiane got to the byline and cut the ball back for the midfielder but the linesman adjudged the ball to have crossed the whitewash, but the closest either side came to a first 45 breakthrough came when Ben Whiteman had a go from the edge of the box and rattled the crossbar with Price scrambling to get back.
That was as good as it got during the opening half, but it only took two minutes of the second to provide a great opportunity for the hosts. Jerome Thomas whipped in a great cross for Gray to get ahead of the United defence and forced Willis into a superb save with a controlled volley.
The chances kept coming for the Eagles and six minutes later a fine clipped pass by Owen Garvan released Thomas, but when one-on-one with Willis he dragged his shot wide of the far post.
Back came the visitors though and after Price had saved Reed's stinger from a tight angle, Connor Dimaio watched a blast from 30 yards flash just wide of the target.
But with 15 minutes to go Palace finally found a way past Willis when Thomas' dangerous in-swinging corner was met by the head of Binnom-Williams at the back post, and the left-back steered it into the bottom corner to hand his side the lead.
That sparked a tame game into life and after Whiteman had a goal correctly disallowed for offside, Sullay Kaikai smashed a venomous 30-yarder towards goal but saw it dip and thud off the crossbar with Willis beaten.
Aiming to kill the game off, Issott's side twice went close in the final few minutes through Ndiane and Gray once again but ultimately one goal proved to be enough.
Palace: Price, Ndiane, Binnom-Williams, Garvan, McCarthy, Inniss (Chambers 46), Boateng (Kaikai 46), Dymond, Gray, de Silva (Sow 80), Thomas. Subs not used: Gregory, Allassani, Black.
Sheffield United: Willis, Paling, Scarisbrick, Dimaio, Berry, Whiteman, Khan, Reed, Cockerline, Calvert-Lewin (Hamilton 65), Coustrain (Kedman 82). Subs not used: Kelly, Ramsdale, Hinchliffe.