A game of few chances looked to be heading West Brom's way after new signing Jay Rodriguez stooped to head them into the lead after 61 minutes -- his first Premier League goal for the club on his home debut.
Ahmed Hegazi was close to making it 2-0 when his header from a Matt Phillips cross was well saved by Jack Butland.
Stoke were given a helping hand in the 77th minute when Hegazi and keeper Ben Foster went for the same ball, leaving Crouch the simple task of heading it into an open goal.
"It wasn't my finest goal, we will take them every day of the week," said Crouch, who came off the bench.
West Brom had been hoping to win their opening three games of a top-flight season for the first time since 1978 and continue manager Tony Pulis's record of never having lost against Stoke City, his former club, as manager.
They managed the latter but will be ruing dropping two points in a game they had seemed to have under control.
Stoke threatened first when Kurt Zouma's deflected shot looked to be spinning under the crossbar until a back-pedalling Foster tipped it over the crossbar.
It was pedestrian fare after that until just past the hour mark when Allan Nyom sped down the right and delivered a dangerous cross which Rodriguez met on the bounce to score.
They could not hold on to the points, although Pulis said he was encouraged by the start to the season.
"I think we had the best chances. You look at the money that Stoke have invested and they are a good side. We wanted Kurt Zouma but couldn't afford that loan fee," he said.
"It's been a great start to the season."
(Reporting by Martyn Herman; Editing by Clare Fallon)
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