The 4-0 victory moved Mauricio Pochettino's men above their opponents in the Premier League table, with Lambert netting the game's second goal shortly after half-time.
His 10th goal of the season came after a chipped pass from England team-mate Adam Lallana, and Lambert made no mistake at the back post with an emphatic finish.
While the 32-year-old was happy to get his name on the scoresheet, it was the performance of the whole team that pleased him the most.
"I think that's probably our best performance of the season," Lambert told Southampton's official website. "Everything went right.
"To a man, we were superb. It's full credit to everyone because it was a great performance.
"We know that we're capable of that because we see it every day in training. We know what kind of players we've got and it's a pleasure to play with them day in and day out.
"It's good to get the rewards with days like that."
Southampton are now two points clear of Newcastle in the league table, and six behind Manchester United in seventh.
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