Substitute Smith halved the deficit 12 minutes from the end, setting up some late drama.
Thankfully, though, the Baggies remained resolute – thanks in part to a late Griffiths save – and saw the game through, claiming victory on their return to Championship action.
Albion: Griffiths, Campbell, Phillips, Mepham, Styles, Iling-Junior (Grant 87), Collyer (Molumby 55), Mowatt, Johnston (Taylor 87), Price (Diakite 88), Maja (Heggebø 68).
Substitutes: Wildsmith, Bielik, Gilchrist, Dike.
Attendance: 24,068 (1,998).