Christian Benteke scored with a deflected shot after 67 seconds to claim his fourth goal in 10 games for Palace, and had chances to improve that tally.
The Belgian striker, 30, had a point-blank header saved by Aaron Ramsdale before firing against a post in the second half.
Captain John Egan spurned Sheffield United's best chance of an equaliser shortly after the interval, slicing over from a corner from six yards out.
But Ebere Eze broke forward late on to convert a second and secure the Eagles' first win in five games, putting them beyond reach of third-bottom Fulham.
That capped a fine performance by the English midfielder, 22, who breezed past Egan in the opening minute before laying off to Benteke, whose shot deflected off George Baldock and over Ramsdale into the Blades' net.
Jeffrey Schlupp's cross then picked out Benteke, who is out of contract this summer, but he directed a free header too close to Ramsdale.
And the Blades offered little in response as their miserable season lurched closer to two unwanted records - most defeats and fewest goals scored in a Premier League campaign.