The Eagles' fifth successive away victory in the league came courtesy of strikes by Andy Johnson, Tony Popovic and Neil Shipperley.
Johnson, who was a constant threat, grabbed his 21st goal of the season when he converted a deflected cross from Danny Granville from close range in the 43rd minute to give the visitors the lead.
Both teams signalled their attacking intentions from the outset, with Popovic putting a free header just wide for the visitors in the second minute.
Two minutes later United's Michael Tonge saw a 20-yard left-foot shot whistle narrowly wide before Paul Peschisolido let fly from distance following an incisive move involving Rob Kozluk and Paul Shaw.
Danny Butterfield almost opened the scoring for Palace when his right-footed shot beat Paddy Kenny and came back off the inside of the post.
With both teams failing to carve out any clear-cut chances and guilty of squandering possession, the game was crying out for a touch of inspiration.
Johnson almost opened the scoring when he pounced on a short header back to Kenny by Kozluk, but the goalkeeper was alert to block with his body.
Butterfield's attempt to lob Kenny from 30 yards saw the goalkeeper backtrack and just manage to tip the ball over before Johnson gave the visitors their half-time lead.
Dean Sturridge should have equalised immediately after the restart when he blazed over with only the goalkeeper to beat after a knockdown from Shaw.
The Blades came to rue the on-loan striker's miss when Popovic doubled the lead on 56 minutes after Kenny flapped at Wayne Routledge's cross from the left and the Australian knocked the ball into an empty net.
A Peter Ndlovu shot which flew just wide gave United some impetus, and a scramble in the box involving Tonge and Peschisolido saw Nick Montgomery's close-range shot hacked away.
Julian Gray should have made it 3-0 when he lofted the ball over the bar with only Kenny to beat.
Although the Blades pushed forward, they failed to create any clear opportunities and were punished when Shipperley converted a cross by former Blade Shaun Derry in the 87th minute.