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.
Source: PA
Source: PA