Premier League - Bent double sinks Norwich
But they had to come from behind after Anthony Pilkington found the top corner with a beautifully struck free-kick in the 25th minute.
But Villa, inspired by the superb Gabriel Agbonlahor, quickly hit back through Bent's tap-in.
Agbonlahor took advantage of calamitous Norwich defending to make it 2-1 three minutes into the second half before the Villa forward notched up his second assist, crossing for Bent to make it 3-1.
Alex McLeish was made to sweat as Villa made life difficult for themselves, conceding to Steve Morison's late header. But Villa survived the grandstand finish to seal an important win that moves them up a place to 8th.
Villa would be in a Champions League position if they had not squandered nine points from winning positions this season, but they started sluggishly against Paul Lambert's ambitious Norwich side.
But Alex McLeish's side looked to have weathered the storm and crafted the first major chance of the game in the 21st minute.
Latching onto Agbonlahor's flick-on, Bent received the ball eight yards out. But the ball was at an awkward height for the England striker, who was denied by John Ruddy, who smothered well.
But just as Villa were stirring from their slumber, Norwich drew first blood - and it was a sensational strike that gave the Canaries the lead.
Pilkington, a £2m summer signing from Huddersfield Town has been key to Norwich's strong form of late and showed his worth in dead ball situations too, exquisitely curling the ball around the wall and into the top corner from 20 yards.
But Norwich were ahead for barely five minutes.
Agbonlahor's driving run down the left had Leon Barnett twisted in knots, before his low drilled cross found Bent steaming ahead of his marker to tap in his fourth of the season.
Having enjoyed the best of the rest of the first half, Villa retained their momentum into the second with Agbonlahor a constant threat.
And he capitalised on suicidal Norwich defending to give Villa a 2-1 lead three minutes into the second half.
Latching on to Barnett's under hit backpass, Agbonlahor nipped in ahead of Ruddy to stroke the ball into the empty net.
Norwich have enjoyed a couple of excellent away days this season - notably at Anfield and Old Trafford - but they were exposed defensively by the searing pace of Agbonlahor, who created Villa's third.
Whipping in a fantastic ball from the right he found Bent, who was able to finish - albeit untidily - from close-range.
The goal put daylight between the teams but Norwich showed courage to continue to attack, and they were rewarded in the 77th minute when Morison found space at the far post to nod in Grant Holt's pinpoint delivery from the left.
The goal made way for a rousing finish as Norwich threw everything at Shay Given's goal.
But Villa held on for a deserved win, which sees them leapfrog their opponents in the table.