Kevin Blackwell's Blades sliced through a troubled Blackpool to take all three points deservedly across the Pennines.
Pool started promisingly and after three minutes former Blades striker Steve Kabba burst passed an onlooking Sun Jihai to force an excellent stop from Paddy Kenny.
Moments later, Kabba was again in with a chance as he rounded Matthew Kilgallon, although this time his effort slipped wide.
It was United who struck first, their three-pronged attack stretching the Seasiders at the back and tricky winger Stephen Quinn was the man who slotted home with a cool right-foot shot.
Pool struggled to string much of substance together, looking disjointed at times and when referee Mr Mathieson pointed controversially to the spot just before the hour Gary Speed stepped up to crash home a well-placed penalty.
The home side bounced back well, the crowd lifted by their best spell of the game and when Kabba collected a Mo Camara cross from 15 yards out he made no mistake in firing home a consolation.
The Blades wobbled at the back and big Ben Burgess popped up at the back post to guide an effort goalwards, United somehow scrambled his effort off the line.
The home crowd were silenced within seconds, the visitors spurred their way up the park to force a counter-attacking corner and as the home side failed to clear, it was Greg Halford who collected at the back post, where he lashed home an effort ten minutes from time, ending any chance of a fightback.