The Blades led twice with a double from Matt Phillips but were pegged back by goals from Clarke Carlisle and Iain Hume.
However, with the points looking set to be shared, Williamson popped up to notch two goals in the last 20 minutes and settle the contest.
Phillips put the visitors ahead after four minutes with a left-footed finish which squeezed inside Iain Turner's near post.
Carlisle brought Preston level in the 29th minute with a downward header from Steven Smith's cross that bounced over Steve Simonsen and into the net.
United regained the lead six minutes before the interval when Phillips combined with fellow Blackpool loanee Billy Clarke to score from eight yards out.
The home side equalized just after the hour when Hume steered the ball home but Williamson restored the Blades' lead with 16 minutes remaining.
And the midfielder's second effort - a fierce drive from 18 yards out - with the final whistle beckoning, put the game beyond doubt.