The Baggies end the away side's unbeaten run and take a victory thanks to the Belgian's late header after a game that was largely a stalemate at The Hawthorns
In a first half stalemate, it was the Canaries who took the lead as Robert Snodgrass saw his free kick palmed into the net, with Zoltan Gera equalizing for the home side just before the break.
The second half was similar, with the Baggies finding a late winner through Romelu Lukaku, who powered home a header.
The Baggies welcomed Foster back into their side after recovering from a groin injury, who replaced Boaz Myhill in one of three changes.
Norwich made just one change from the side that beat Wigan, with Grant Holt replaced up front by Steve Morison, having failed to recover from a knock.
The home side started with a great deal of intent, and after just a couple of minutes saw Romelu Lukaku head wide from a superb cross by Goran Popov.
They then began to enjoy the majority of early possession, but the Canaries made it very difficult for West Brom to penetrate their solid and patient defense.
It took until the 21st minute for either side to create another chance, as Lukaku was played in early by James Morrison but his low shot was saved well by Mark Bunn.
The away side then gained a free kick from 25 yards out, and returning goalkeeper Foster could only succeed in palming Snodgrass’ effort into the net, giving Norwich a 1-0 lead.
This seemed to galvanize the Baggies, who then won a corner that was delivered well by Chris Brunt and should have been turned home by Gareth McAuley.
The home side then created another good chance as after more good work from Morrison, the ball was played back to the impressive Goran Popov, who blazed a fierce shot over the bar.
Norwich was holding out well but could not managed to maintain its advantage, as in the 42nd minute a Brunt corner caused havoc in their box and was turned home by Gera.
It took until the 54th minute for either side to create a chance, as Steve Morison was played through by Alexander Tettey but saw his shot well blocked by McAuley.
From the resulting corner, a delicious cross from Snodgrass found Michael Turner at the back post, but he put his free header wide of the target.
However, both sides struggled to make any impact with their forward play, even with the Baggies having brought on Marc-Antoine Fortune and Shane Long.
A superb chance presented itself for the home side in the 71st minute as it won a free kick right on the edge of the Norwich area, but Peter Odemwingie blasted it into the wall to the frustration of Brunt.
The Baggies were continuing to press forward and pressure the away side, and broke the Canaries’ resolve in the 82nd minute as Lukaku headed home powerfully to give his side all three points.