Treacy, who had a spell on loan at Bramall Lane last season, opened the scoring in the 55th minute on Saturday with a speculative long-range shot and then added a second from distance 13 minutes later.
United hit back through Jordan Slew with 18 minutes remaining but North End substitute Nathan Ellington added a late third.
The result condemned Micky Adams’ side to a fourth straight defeat but was a massive boost to Preston as they recorded their third successive home victory.
Preston made an encouraging start and went close inside the second minute when Treacy delivered a corner from the right flank.
Striker Chris Brown rose to meet the ball with a firm header but his effort flew wide of the mark from 12 yards out.
Moments later Treacy collected possession and engineered the space to hit a shot from the edge of the 18-yard box which flew just wide.
Preston continued to build up a head of steam and threatened the visitors’ goal again in the fourth minute when Iain Hume drove a 20-yard strike wide.
The Blades gradually steadied themselves and Stephen Quinn threatened with a shot from distance which forced Preston defender Craig Morgan into a fine block.
Having survived the early bombardment, the visitors began to grow in confidence and midway through the first half they went close twice in quick succession.
First rookie defender Harry Maguire struck a fierce long-range effort which flew over the crossbar and then Quinn threatened again from distance.
The Blades carved out their clearest opening yet in the 29th minute when Slew drilled in a low shot from the edge of the box which drew a fine parried save from Preston goalkeeper Iain Turner.
However, the pendulum gradually swung back in Preston’s favour and Eddie Johnson went close with a long-range strike and then Brown missed the target from just 12 yards out.
Neither side could break the deadlock before the interval, despite North End striker Brown again going close just before the break.
However, that changed 10 minutes after the restart when Treacy seized possession and struck a low, left-foot shot into the bottom corner from around 30 yards.
The strike sent Deepdale into raptures and it got better for the hosts in the 68th minute when Treacy was again given the time and space to fire a right-foot shot into the top corner from 18 yards.
Yet the Blades refused to lie down and hit back with 18 minutes remaining when Slew hit an 18-yard shot into the bottom corner to give his side hope.
Five minutes later Darius Henderson cracked a shot against the post from 12 yards but Ellington eased home fears in the last minute when he fired home right-footed from the edge of the 18-yard box.