Villa fell behind early on at the Madejski Stadium but responded quickly through Christian Benteke.
Lambert believes that his side have finally been rewarded for their confident, spirited approach to fighting for survival.
He told Sky Sports News: "It is never easy at the best of times with the position we are in, but the lads were fantastic today, we deserved to win.
"To lose an own goal was a blow but the way we bounced back was terrific and I am very proud of my players tonight, they deserve so much credit.
"I see a lot of confidence in the players, they have been playing really well without the rewards. The goals that we scored today were excellent, we don't look like a team that looks like it is fighting for its life. There will probably be a few teams looking over their shoulder tonight and we have a bit of momentum at the minute."
Villa are now three points clear of the drop zone but have played a game more than Wigan Athletic in 18th place.