The home side had to come from behind after Anthony Pilkington’s superb free-kick but they were level when Bent side-footed home.
Agbonlahor then took advantage of Leon Barnett’s poor back pass to give Villa the lead before setting up Bent again.
Steve Morison set up a nervy finish when he headed home from close range.
The win was Villa’s third of the season and ended a three-game winless streak – but it was nothing more than the home side deserved.
Bent and Agbonlahor were in sparkling form, giving England manager Fabio Capello a timely reminder of what they’re capable of ahead of the announcement of his squad for the friendlies with Spain and Sweden.
For the second week in a row Villa started slowly with Pilkington forcing Shay Given into a good early save.
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Moments later Morison should have done better when he was given space in the box but his shot, on the turn, was straight at the Villa keeper.
The home side created a good chance five minutes later when Bent was through one on one with John Ruddy but the Norwich keeper raced off his line and deflected the shot clear.
The deadlock was broken on 25 minutes when Pilkington made the Canaries’ domination pay and struck a sublime free-kick into the top right-hand corner.
The goal was the 300th Premier League goal of the season and one worthy to hold such a title.
But the lead lasted just five minutes when Bent scored for the third home game in a row.
All the hard work was done by his strike partner Agbonlahor, who played in a superb low cross from the left to present Bent with a chance he couldn’t really miss from four yards out.
Bent and Agbonlahor were looking threatening every time the home side went forward and the latter was on the scoresheet himself two minutes after the restart.
A weak back pass by Barnett gave Ruddy no chance and he could only watch on in horror as Agbonlahor nipped in first and fired into an empty net.
The all-important third goal for the home side came on 62 minutes and it was nothing more than they deserved after some excellent attacking football.
A run from Charles N’Zogbia was cut out by the Norwich defence but Agbonlahor picked up the loose ball and swung in another superb cross, which found Bent six yards out and he side-footed home.