Villa arrived at the Britannia Stadium inside the Premier League relegation zone, but buoyed by two wins in their previous three outings.
And Villa made that three in four as they moved out of the bottom three with a dramatic late surge against the Potters.
A spectacular 87th-minute strike from Matthew Lowton and a stoppage-time effort from Christian Benteke saw Villa secure a victory that their manager feels was 'thoroughly deserved'.
Lambert told Sky Sports: "I thought we deserved it. I thought we were terrific in certain parts of the game. For the majority of the game I thought we were outstanding and I thought we thoroughly deserved to win the game.
"And the three goals, especially Matty Lowton's - I don't think you will see a better goal in Europe, let alone Britain.
"It was a world-class finish. He has come from Sheffield United this season, not missed a minute in the games and that was one unbelievable finish."
Lambert hopes the momentum Villa have been able to build over recent weeks can carry them to top-flight safety, with there now just six games of the season remaining.
He added: "We are playing very well at the minute.
"I thought we were unfortunate to get beat by Liverpool (last weekend), but it's not every week that you have to play Liverpool and I thought today that, right from the off, we were outstanding."