The Midlands side made the most of James Perch's first-half dismissal with strikes from Dave Edwards and Helder Costa in the space of eight second-half minutes before Joel Lynch grabbed a last-minute consolation for the hosts.
The victory over the Hoops marked Lambert's first win since taking charge of Wolves and brought an end to their nine-game winless streak in the Championship.
"We should have been 5-0 up," Lambert told reporters afterwards. "Unbelievable. We had three or four one-on-ones and should have finished the game.
"I thought we earned the right to win the game with the start we had. We had one or two chances before the sending off against a team that's really difficult to play against, a small ground with the crowd on top of you. It's a terrific win. I thought we deserved to win.
"I've only been here two and a half weeks and we've had a draw and a loss. There's a lot of hard work to be done and we have to try and get to January and get a bit of help in. But the nucleus are good players."
The result saw Wolves move up to 19th in the table, three clear of the relegation places.