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.
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.
- Sports & Recreation
- Youssouf Mulumbu
- Artur Boruc