The home side got off to a flying start when Ashley Westwood put them ahead inside the first minute, before Jordan Bowery - on as a substitute for the injured Gabriel Agbonlahor - turned the ball into his own net on 28 minutes.
Andreas Weimann's brace of headers late in the first half put Villa in control at the break, and they comfortably saw the game out in the second period to virtually secure their top-flight status.
Lambert's men are now six points clear of Norwich City with two games remaining, and look certain to stay up courtesy of their vastly superior goal difference.
"(It was) massive," he said. "I've just said to the lads in there, I've been involved in massive games before but the pressure on that one was incredible.
"They came through that, and if they come through that then they can come through anything in their career.
"I thought they were outstanding and I thought we deserved to win the game.
"We started the game great then we lose one of our main players (Agbonlahor) to injury which puts you on the back foot.
"But after that I thought we were fantastic, I really did. Every one of them was excellent and it was a huge performance."
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
