Russell Hoult became only the second visiting keeper to leave Carrow Road with a clean sheet this season.
His team left with a point thanks in no small measure to some controversial refereeing decisions.
The most notable came late on in the game when Mathias Svensson appeared to be fouled in the West Brom penalty area but was booked instead of Thomas Gaardsoe who had hauled him to the ground.
The Canaries enjoyed most of the early possession without troubling Hoult.
When Albion hit back, Jason Koumas was inches away with a low shot before the Welsh international brought a fine save from Robert Green.
Craig Fleming rescued Norwich with a goal-line clearance after Delroy Facey had got the ball past Robert Green who had rashly come to the edge of his penalty area.
Gary Holt, Norwich's man-of-the-match, did well to nick the ball away from Facey and Geoff Horsfield fired wide when well-placed.
Hoult then saved a bullet header from Damien Francis which flew into his midriff.
Referee, Brian Curson, then amazed the home fans and viewing pundits when he failed to penalise James Chambers for a professional foul on Darren Huckerby. Holt was booked for voicing his feelings on the matter.
The visitors goal then led a charmed life as three shots were blocked before Jim Brennan headed inches wide.
Norwich enjoyed most of the second-half possession but had only a growing tally of corner kicks to show for it.
Svensson was again wrestled to the ground by Gaardsoe just outside the penalty area but Mulryne's resulting free-kick cleared the crossbar.
Huckerby had a shot blocked in the closing stages but that was the last chance for Norwich to collect all three points.