United rarely looked like surrendering their advantage thereafter and added a second in stoppage time when Stephen Quinn finished coolly after being set up by Williamson.
The hosts will probably feel they should have wrapped up the points before Quinn's late strike, with Ched Evans and Jamie Ward both guilty of wasteful finishing more than one occasion.
The victory lifted Kevin Blackwell's side above the Eagles in the table and moved them to within touching distance of the play-off places.
Palace, meanwhile, still appear to be lacking the consistency required to mount a genuine promotion push.
United boss Blackwell made just one change to the side that were held to a goalless draw by Nottingham Forest in midweek, with Williamson replacing the suspended Nick Montgomery in midfield.
Davis and Alan Lee were recalled to the Palace starting XI in place of Nathaniel Clyne and Calvin Andrew, who were both named among the substitutes.
The hosts enjoyed the better of the early exchanges, with Ched Evans seeing a shot blocked by Danny Butterfield and Jamie Ward testing Eagles goalkeeper Julian Speroni from 20 yards.
Palace responded with Jose Fonte firing a left-footed shot straight at Mark Bunn from the edge of the area.
But United went in front in controversial fashion soon after.
Williamson prodded Quinn's cross beyond Speroni, only for Palace defender Davis to scramble the ball clear.
However, following consultation with his assistant, referee Colin Webster decided the ball had crossed the line and the home fans duly celebrated.
The hard-working Evans came close to adding a second for United seven minutes later, only for Speroni to hold his close-range volley from Ward's corner.
In-form Eagles midfielder Darren Ambrose then curled a free-kick over the bar, while Williamson also failed to keep the ball down when volleying goalwards from 12 yards in the 39th minute.
Ambrose did not re-appear after the interval, with Sean Scannell coming on in his place.
The Blades started the second period brightly and Evans saw another chance go begging when he fired wide following good work from Quinn.
Butterfield left the field due to injury in the 55th minute, with Clyne the man to replace him.
Chances were few and far between as the second half wore on, although Blades full-back Kyle Walker thundered a powerful effort over the bar with 17 minutes remaining.
Victor Moses and Neil Danns had chances at the other end, but neither was able to trouble home goalkeeper Bunn.
And although Ward spurned a golden opportunity to put the seal on United's victory, it mattered not as Quinn grabbed a second goal at the death.