Lambert drove home from 15 yards, four minute before the break after Graeme Murty and Papa Waigo combined to set up the deadly marksman.
Saints should have had the result done and dusted on countless opportunities after half-time with Lambert, Adam Lallana and substitute Michail Antonio all guilty in front of goal.
After a dull opening 20 minutes Alan Pardew's side breathed some life into the game as Lallana's skill took him into space but the much-coveted midfielder could not find the target.