Odemwingie put a difficult week behind him, which had seen Nigeria fail to qualify for the African Nations Cup and further concerns over his ankle problem.
He came off the bench to score his second goal of the campaign.
Albion boss Roy Hodgson said: "It will give Peter a big lift. He was terrific when he came on.
"I was preparing for the game with Somen (Tchoyi) because I didn't think Peter was going to be fully fit and that turned out to be the right decision.
"He's a very good player and it's important for him to realise we are all behind him and it is not on his shoulders (to score all the goals).