West Brom lost again after Bournemouth came from behind to win 2-1 on Saturday.
Jay Rodriguez's close range shot beat Asmir Begovic to put the Baggies ahead minutes into the second-half.
Jordan Ibe then responded when he struck with just over ten minutes remaining. Junior Stanislas fired in a late winner to inflict more misery on Alan Pardew's men.
Cherries boss Eddie Howe said: "I'm thrilled with us producing another comeback. Trust me, we don't want to do it that way, but at this point of the season I think I'll take any way if it means us getting three points.
"West Brom made it tough, they are a very experienced side, they have very experienced Premier League players and an experienced manager, so it was hard to find a way to win against them.
"It was important to get a result today off the back of the Tottenham and Leicester games. I thought we played very well in those games and today we didn't.
"But football has a strange way of working like that. We want to try and win every game and there's only seven to go now."