Andy Monkhouse fired relegation-threatened Pools into a shock lead inside the opening 10 minutes as he swept home from five yards following a neat passing move.
Lee Barnard equalised just three minutes later, heading into an empty net after Jason Puncheon had been denied by the crossbar.
Lambert gave the hosts the lead in the 38th minute with a clinical half-volley following a period of sustained pressure.
Papa Waigo increased Saints' advantage to 3-1 in the 56th minute after Puncheon's run and Peter Hartley's dreadful error.
Neil Austin ensured a nervy final 30 minutes for play-off chasing Southampton as he planted an 18-yard strike into the top corner, but the hosts held on.