Mauricio Pochettino's side enjoyed 77 per cent possession in the Barclays Premier League clash, having 21 shots and completing almost six times as many passes as Villa.
Libor Kozak nodded home Villa's second after Jay Rodriguez levelled, although Saints drew parity again through Dani Osvaldo.
Lambert's side would not be denied, though, scoring against the run of play but in some style, with Fabian Delph's wondrous strike from distance proving the difference.
"You show me a stat that wins you a game of football and I might try and buy it," Lambert said of the one-sided match facts.
"I've had pats on my back in certain games when we've been turned over. It is not what you look for - you try and win.
"I thought we deserved to win the game. There have been times when we have had loads of the ball and got nothing. All you get is a pat on the back.
"We needed three points and I thought we were lethal in front of goal.
"I thought Agbonlahor's goal was world class - when he is like that with his speed and power there are not many people can catch him.
"The second goal was a terrific header from Kozak and the third goal was worthy of any win.
"I think we should have had a penalty when Christian Benteke gets brought down, so I am delighted with the lads."
Benteke was introduced as a second-half substitute after Lambert boldly decided to drop the Belgium international after seven scoreless matches.
"The football club does not revolve around one player," he said. "I made a decision that I thought was the right call.
"We have 25 lads and I try and treat them the same way. Christian was brilliant last year but has had a little spell when at the minute he has not been hitting the heights of last year.
"But when he came on I thought he looked as if he was getting back to the powerhouse he is.
"Sometimes a rest is as good as playing sometimes. We have seven games this month. Kozak led the line great and got the goal."
The only negative on the night for Villa was an injury to captain Ron Vlaar, who was forced off at half- time with a calf complaint that will be assessed on Thursday.
Saints also picked up knocks in the match, with Victor Wanyama and Nathaniel Clyne to be reviewed after being forced off.
Pochettino is unsure of the extent of those injuries and downplayed an altercation involving club record signing Osvaldo at the end of the match.
As tempers frayed after the final whistle, the Saints boss came onto the pitch to usher away the booked Italy international from a scuffle.
"It's only normal in football," Pochettino said. "We're angry. Emotion gets the better of you, so it's normal there were temper tantrums at the end."
What was of more concern to the Southampton manager was falling to a third successive defeat for the first time in his St Mary's tenure.
"It is a difficult result to take because the team put in a great effort and did very well," Pochettino said.
"It's the type of game you lose maybe once in 1,000, but tonight we lost it."
- Sports & Recreation
- Mauricio Pochettino
- Gabriel Agbonlahor