Lambert started from the bench against Norwich but made an impressive impact when brought on early in the second half for Adam Lallana.
A minute after his introduction, the forward added to Morgan Schneiderlin's early strike and then showed impressive composure to provide the assist for Jay Rodriguez in front of on-watching England manager Roy Hodgson.
"I am always pleased to score a goal," he said. "I was determined to get on and do well for Southampton first and foremost and help the team get the points.
"Of course, I am still hoping to get to Brazil. It is my dream and everyone's dream so that is obviously at the back of my mind while I am trying to do well for Southampton as well."
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