The Canaries had to deal with a rampant Baggies outfit early with Andrew Surman clearing James Morrison's sweetly struck half-volley off the line in the 32nd minute but just over ten minutes later, Paul Lambert's men were in front thanks to a lovely Surman volley from a chipped Wesley Hoolahan ball from the right.
In the 67th minute, Norwich defender Daniel Ayala made a very poor challenge on Jerome Thomas with referee Mike Dean pointing to the spot. Shane Long, who had only been brought on five minutes earlier, stepped up and cheekily stroked past John Ruddy for the leveler.
West Brom pressed and pushed for a winner but as they strived for maximum points they were caught on the break in the 79th minute with skipper Grant Holt supplying the final ball from the left for Steve Morison to head home for his eighth of the season.
Norwich have experienced just one defeat in their last seven games to maintain their ninth position whilst Roy Hodgson's Baggies stayed 15th following a third straight loss.
TRIBAL ASKS: Norwich continue to record the results that will keep them up. Does Lambert have a squad capable of achieving that? Where to now for West Brom? Are they in danger of soon falling into the bottom three
The Hawthorns, West Bromwich - 22,474
Yellow cards:WBA - nil NOR - Daniel Ayala 67'