The 26-year-old scored in the 89th minute to claim all three points for the away side, dragging them further away from the drop zone at the expense of Lambert's former club
The Canaries looked to have claimed a hard-fought point after Grant Holt fired home a penalty with just over a quarter of an hour remaining, but Agbonlahor popped up late on to steal the win.
The home team made three changes from the side that lost to Stoke last Saturday, with Steven Whittaker, Alexander Tettey and Kei Kamara all dropping out and replaced by Javier Garrido, Anthony Pilkington and Kei Kamara.
Former Carrow Road gaffer Paul Lambert, as predicted, stuck with the same starting line-up that put six past Sunderland on Monday night to help their chances of remaining in the Premier League next season.
Norwich had the better of the opening period, with Scotland international Robert Snodgrass going close with a strike which was deflected for a corner.
The visitors started to get back into the game and almost took the lead, but Agbonlahor’s strike towards goal was deflected away behind for a corner by Sebastian Bassong.
Two minutes later the Norwich fans were up off their feet demanding a penalty as a Pilkington cross appeared to strike the arm of Matthew Lowton, but referee Kevin Friend waved away the protests.
The game became quite scrappy for the remainder of the half, with play congested in the middle of the pitch, while visiting keeper Brad Guzan's only action of note was to claim a Pilkington cross just ahead of the lurking Holt.
As the first half entered stoppage time, Aston Villa almost took the lead as an Agbonlahor cross from the right cannoned off Garrido and onto the top of the Norwich bar.
It took just 10 minutes for Villa to claim the lead they deserved in the second half, though, as Agbonlahor received possession in the middle of the Norwich half, striding forward with defenders backing off him, before unleashing a low effort into the bottom corner.
Aston Villa should have extended their lead when Agbonlahor raced down the left, before playing the ball into the box for Andreas Weimann, but he could only direct his effort over Bunn’s bar.
However Lambert’s side were lucky not to be reduced to 10 men when Christian Benteke seemed to grab Bassong by the throat after the two squared up, but the Belgian striker got away with a booking.
Norwich were handed an equaliser with 18 minutes left in the game, as Snodgrass came in from the right hand side and was hauled to the ground by Joe Bennett, allowing Holt to fire home the resulting penalty and level things up.
With the game approaching injury time, the visitors grabbed a dramatic, late winner as Agbonlahor got goal-side of his marker Bassong before sliding the ball beyond Bunn to seal a vital victory that virtually guarantees their safety.