The Blades sank lower down the Championship table following the defeat, although they clearly missed captain Chris Morgan's presence at the back.
Morgan has been ruled out for the season due to a cruciate knee ligament injury and United's makeshift defence were the architects of their own downfall as they allowed Jake Livermore too much space too tee up Priskin who netted an early opener from close range.
Stephen Quinn grabbed a deserved equaliser midway through the first-half after a good spell of pressure from the Blades.
However, McAuley scored what turned out to be the winning goal when he was given space to bring down Grant Leadbitter's cross and fire past United goalkeeper Steve Simonsen.
Ipswich have been struggling away from Portman Road this season so it came as a surprise that they took the lead with their very first attack in the sixth minute.
The United defence failed to clear their lines following Carlos Edwards' long throw and an unmarked Livermore headed the ball into the path of Priskin, who turned and shot past Simonsen from close range.
United defender Johnny Ertl nearly headed the ball into his own net from another Edwards long throw and Damien Delaney headed over from the resulting corner.
The visitors were looking threatening every time they attacked and Priskin almost doubled his side's lead but the Hungarian international struck the outside of the post from an acute angle after shaking off the challenge of Ertl.
To their credit, the hosts upped their game and their pressure nearly told as Richard Cresswell's header from Jamie Ward's left-wing cross was cleared off the line by Tom Eastman.
United's downfall this season has been their lack of goals - with just nine strikes in 14 games. However, they were rewarded for their efforts after 29 minutes.
Mark Yeates' cross was cleared into the path of Stephen Quinn and the midfielder made no mistake in drilling the ball home from 12 yards.
The Blades though failed to seize the initiative and they fell behind for a second time five minutes before the interval.
Leadbitter's right-wing cross fell to McAuley, who was in acres of space in the area and the defender made no mistake by blasting past Simonsen.
Yeates shot over from 20 yards as the Yorkshire club immediately looked to level matters.
Kyle Bartley then brought the ball forward from right-back and unleashed a shot from 30 yards which Town keeper Martin Fulop tipped on to the post.
McAuley nearly grabbed his second against the run of play with an unmarked bullet header from Colbeck's corner, however, Simonsen was able to hold the effort.
Substitute Ched Evans volleyed wide from 20 yards as Gary Speed's men laid siege to the Blues' goal.
The young striker's tame shot was easily saved by Fulop when one on one in injury-time and Ipswich were able to withstand the barrage and claim their first victory over the Blades in nine attempts.