West Brom ended Norwich's six-match winning run as they took a well-deserved point at Carrow Road.
Dara O'Shea was left unmarked six yards out at the back post to head in John Swift's inswinging free-kick and give the Baggies an early lead.
Gabriel Sara almost levelled on his first league start of the season when his angled shot hit the bar.
West Brom looked comfortable, but were held to their seventh draw of the season when Teemu Pukki's goalbound shot struck team-mate Sam Byram and wrong-footed goalkeeper David Button.
Conor Townsend made a goal-saving challenge to deny Byram, and Button saved from Kieran Dowell, but a late Norwich winner would have been harsh on Steve Bruce's side.