The battle between Marcondes and Griffiths continued straight after the interval. This time the shot-stopper came out on top again, pushing away a whipped free-kick.
Norwich defender Harry Darling fired one effort wide, and flicked another inches past the far post, midway through the second period as City searched for an equaliser.
But Albion regained control to frustrate the hosts. And despite a late onslaught where Griffiths made two outstanding saves and the Baggies cleared off their line, the visitors just about held firm, earning an outstanding win.
Albion: Griffiths, Campbell, Phillips, Mepham, Taylor (Bielik 75), Molumby, Mowatt (Collyer 75), Iling-Junior (Gilchrist 85), Price, Johnston (Wallace 60), Maja (Heggebø 60).
Substitutes: Wildsmith, Styles, Diakite, Bostock.