Foster was called into action as early as the 7th minute to palm away a Steven Pienaar header and, only a minute later, he stopped another long range effort by the Everton midfielder.
The save of the match came just after the half hour as Foster athletically tipped over a driven shot by Kevin Mirallas.
But when the Baggies keeper was taken off with 12 minutes remaining after suffering an ankle injury Everton turned the screw. This time the woodwork came to the visitors’ rescue.
Marouane Fellaini struck the inside of the post with minutes remaining before wing-back Seamus Coleman hit the underside of the bar in stoppage time.
Baggies boss Steve Clarke was deeply concerned about Foster’s injury.
“He felt a pop in his ankle,” he said.
“It’s an injury we have to be a little bit worried about.”