Andy Reid, on loan from Sunderland, fired the Blades - who have now lost on their last five visits to Carrow Road - ahead in the 17th minute with a fantastic 25-yard free-kick but defender Michael Nelson headed Norwich level within three minutes.
Richard Cresswell, on his return from suspension, put United back in front after 29 minutes although Norwich replied for a second time in the 64th minute when Hoolahan converted from the penalty spot.
Hoolahan then grabbed the winner with six minutes left with his second spot-kick conversion after Kyle Bartley was penalised by referee Phil Crossley for handball.
The Blades then finished the game with 10 men when Stephen Quinn was sent off for violent conduct after a bad foul on Hoolahan, who duly claimed the match ball in injury-time.
The visitors made a bright start and Reid saw his third-minute volley from 20 yards saved by City goalkeeper John Ruddy.
Nelson headed a David Fox cross over the bar for Norwich, who enjoyed the majority of the early possession, before the Blades threatened again when Mark Yeates fired a shot wide from 18 yards.
But United took the lead in the 17th minute.
Jens Berthel Askou was penalised for a foul on Ched Evans and from the resulting free-kick, Reid beautifully curled the ball into the top corner for his first goal in six games.
However, their lead was shortlived as the Canaries got themselves level within three minutes.
Fox delivered a free-kick, after Nick Montgomery fouled Chris Martin, and Nelson was on hand to head home from six yards for his second goal of the campaign.
The goal seemed to spur Norwich on and Nelson nearly repeated the trick in the 24th minute but this time he headed wide before captain Grant Holt also headed wide from another Fox delivery.
But the Blades regained the lead in the 29th minute through Cresswell, who struck home from 12 yards after good work from Quinn.
Norwich boss Paul Lambert brought on playmaker Hoolahan for Simeon Jackson at the break and the Irish midfielder pulled the home side level for a second time in the 64th minute.
Montgomery brought down Holt, and was booked in the process, with Hoolahan making no mistake from the spot.
Evans unleashed a shot from 35 yards which was comfortably dealt with by Ruddy and Steve Simonsen made a fine save from Martin at the other end.
Yeates then fired over from 18 yards and Martin headed over from a corner from substitute Anthony McNamee as the game swung from end to end.
Berthel Askou was denied by Simonsen with 11 minutes left and Evans blazed over when well placed as both sides went for a winner.
That came when Hoolahan pounced with his second penalty and there was still time for Quinn to see red.
Hoolahan wrapped up the points to claim his hat-trick on a breakaway deep into injury time.