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 levelled 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."
- Sports & Recreation