After a largely uneventful game, Kenwyne Jones had the chance to win it for the home side late on but the striker’s tame effort was gathered by Ben Foster.
The draw moves Stoke into the top half of the Premier League table in 10th place, while West Brom stay in eighth.
After watching his side pick up their first point in three league outings, Pulis told BBC Sport: “It was a very honest, committed game with very few chances. Probably the best opportunity fell for Kenwyne Jones right at the end.
“The greatest thing about today was the crowd turned up and were great. There has been a bit of discontent around the place but they were fabulous from the first minute to the last minute.”
Get enhanced odds of 7/1 on Rangers to get promoted on Thursday with Paddy Power.