The Saints deserved their victory after dominating the game. Skipper Adam Lallana had a goal ruled out in the first-half for off-side after tapping in a flick on from Lambert.
Replays showed that Lallana may have been level when he slotted in from a yard out.
Saints also hit the woodwork through Rodriguez with a fizzing volley from just inside the area after a poor Albion clearance.
Steve Clarke’s side had little to show from their efforts aside from a late Billy Jones header which was brilliantly kept out by Artur Boruc.
PRE-MATCH: Victor Wanyama and Nicolas Anelka make their debuts – Wanyama started in the Saints midfield following his switch from Celtic. And it was the return of the player they call Le Sulk as Anelka led the line for the Baggies.
32’ GOAL RULED OUT: Adam Lallana thought he had given Southampton the lead when he taps in Rickie Lambert’s flick-on but the linesman raised his flag. But the replays show the skipper may have been level.
52’ CROSSBAR: Jay Rodriguez crashes his volley from just inside the area against the crossbar after a poor Albion clearance.
89’ GOAL: WBA 0-1 Southampton - Rickie Lambert slams home a penalty a minute from time after Luke Shaw is brought down in the box.
90+1’ MATCH-WINNING SAVE: Artur Boruc produces a stunning save to keep out Billy Jones’ header.
TALKING POINT: The age-old offside debate. Adam Lallana may have been level when he side-footed in Lambert’s cross with the benefit of TV replays. Jay Rodriguez was in an off-side position but did not touch the ball. Cue calls for more technology.
Rickie Lambert scored his 94th goal for Southampton in 171 games with a confident penalty.
Albion have won just twice on the opening day in the past 16 seasons.
MAN OF THE MATCH
Adam Lallana (Southampton). Was a constant menace with his mazy runs and provided good service to the strikers.
SOUTHAMPTON: Boruc 8, Chambers 5, Fonte 6, Lovren 5, Shaw 6, Wanyama 6, Schneiderlin 4, Ward-Prowse 6, Lallana 8, Rodriguez 7, Lambert 7… Subs: Ramirez 4, Cork 4, S. Davis 5.
WEST BROM: Foster 5, Jones 6, McAuley 5, Olsson 6, Ridgewell 5; Morrison 5, Mulumbu 4, Yacob 5, Dorrans 5; Anelka 6, Long 5. Subs: Vydra 4, Rosenberg 4.