Lambert's side found themselves 2-0 down after nine minutes at Villa Park but they responded impressively to earn the victory, with Christian Benteke scoring the winner from the penalty spot.
"All credit to the team, the response was fantastic," the Villa boss told reporters after the West Midlands derby. "With derby games, it doesn't matter where you are in the table, they're really unpredictable.
"We've done so much in a short space of time. We have a young side and we are giving it a right good go."
Villa have climbed to 10th in the Premier League following the win.