The result was greeted by huge relief by Villa, who began the game in the bottom three, but it also pulled Stoke into the scrap after a run of one win in 13 games.
Lambert said: "I thought we were the better team throughout the game. I thought we were absolutely brilliant right from the off. We looked a threat the whole game. There were some colossal performances out there. I am proud of the lads.
"After going to 1-1 we still kept on going. The second goal - I don't think you'll see a better goal in Europe, let alone Britain.
"The technique and the actual finish were just world class.
"Villa have spent most of the season fighting at the bottom end of the table and, along with the likes of Southampton and Wigan, have found some form at the right time."