Villa, who had thumped Sunderland 6-1 on Monday night, moved onto the fabled 40-point mark with a battling display to sink the Canaries, who are still looking anxiously over their shoulders, now just three points clear of the drop zone heading into the final two matches.
Following a decent first half by the home side, Villa winger Agbonlahor drilled in a superb 25-yard effort on 55 minutes.
Norwich captain Grant Holt leveled from the penalty spot, but the Canaries could not hold on for a point as Agbonlahor rolled in a late winner following a quick break.
"We had to win, and it was a big effort, especially after Monday night," said Lambert, whose side are five clear of 18th-placed Wigan, albeit having played a match more.
"The character and the mental strength we showed in the second half was outstanding.
"Gabby has been on fire for most of the season, and we have goals in us.
"I don't know if 40 points will be enough, but from everybody saying we were dead and buried, were too young and were not going to do it.. we are now playing every so well.
"We have a really tough game next week (against Chelsea), but we have a lot of confidence in the side, and if we can keep that and keep building the football club, then we will have a great future."
Scotsman Lambert had guided Norwich to successive promotions back up into the top flight before an acrimonious departure last summer, but has now won twice on his old stomping ground following Villa's Capital One Cup quarter-final win in December.
The former Celtic man, though, insists that is all very much water under the bridge, with compensation finally settled by both parties for his move to Villa Park.
"Chris Hughton is a terrific manager and this is a terrific club," said Lambert, who put up with a bit of well-natured banter from the home supporters behind the dugout.
"I had a great rapport with the fans when I was here and it was a really great time.
"Nothing should blight the relationship I had with the Norwich crowd, but things happen, it got sour and you have to move on, that's football."
While Villa will now be hoping they have done enough to avoid a last-day scrap for survival when they travel to Wigan, Norwich must beat West Brom at home next weekend to avoid a nervous final outing at Manchester City.
Hughton's men have struggled for consistency since their 10-match unbeaten run ended, winning only twice in 2013.
"We are massively disappointed and frustrated," said the Norwich manager.
"It was a game I don't think we deserved to lose.
"We were very good in the first half, but we knew what Villa's strengths were, and the quality they have.
"We kept them quiet for most of the game, but conceded two poor goals.
"We were a threat in the final third, but you have got to score goals, which has been difficult for us."
Despite Norwich's poor run of form, Hughton remains optimistic.
"We are in a battle, we know that, but it is still in our hands," he said.
"We have two games left, the next is at home to West Brom, so we need to make sure we dust the players down and make sure we show a lot of the good things which we did do, because we will need every bit of that next week."
Norwich later confirmed on their official website that their end-of-season awards dinner, planned for Monday, had been cancelled, to allow those involved to concentrate on the West Brom game.
The Canaries also confirmed forward Kei Kamara would return to Major League Soccer club Sporting Kansas City following the end of his loan spell.
The Sierra Leone international moved to Norfolk at the end of the January transfer window, playing 11 times in the Premier League, and scoring in the 2-1 win over Everton at Carrow Road on February 23.
Robb Heineman, CEO of Sporting Club said that the Canaries had declined the option to extend Kamara's stay.
Kamara took to Twitter to thank the club and supporters. He said: "I want to thank the Norwich City organisation for everything they did for me. Not everyone gets to live their dreams, but they gave me mine.
"Also thank you to all the fans in the UK especially in Norwich, Norfolk for welcoming me with warm arms. Top class people/fans.
"Will always have a place in my heart for Norwich. #HeartShapedHands to all u guys & I wish the boys best of luck in next 2 weeks. God bless."
Kamara could return for Sporting as soon as Wednesday against the Seattle Sounders.