Lambert, who headed the winning goal in midweek against Scotland with the first touch of his England debut, coolly dispatched the spot-kick in the 90th minute after Luke Shaw had been brought down in the box by Youssouf Mulumbu.
It sealed a deserved three points for the Saints, who had been the better side for most of the contest.
They had their goalkeeper Artur Boruc to thank as the death, though, as the Poland international pulled off a great save to keep out Billy Jones' header.
There appeared to be signs of early-season nerves in the opening stages of the game, with West Brom's number one Ben Foster making a hash of an attempted catch and Boruc then giving away a corner by fumbling a James Morrison shot.
Southampton did seem to be settling quicker, however, and Foster's palms were stung by a long-range James Ward-Prowse effort just before the quarter-hour mark.
At the other end Gareth McAuley nodded a Graham Dorrans corner well over, but Southampton were soon pressuring again.
Ward-Prowse's free-kick into the box fell to Lambert, who saw his shot on the turn well blocked by McAuley, and a scramble ensued, with Adam Lallana also striking the ball against a Baggies shirt before the hosts got it away.
Albion attempted to get a grip on the game and when Jonas Olsson nodded the ball to Mulumbu from a free-kick, the midfielder struck an effort wide off one of his team-mates.
Southampton then had the ball in the net as Lambert headed a delivery from Calum Chambers - making his first senior Saints start - back across the area for Lallana to poke in at the far post, but the assistant referee's flag was raised.
Source: PA
Source: PA