West Brom brought back Joe Carter, who had been absent with a knee injury since the semi-final, to replace Harry Jones.
West Brom also left out Arthur Gale who had played in all six FA Cup ties that season and scored four goals from the right wing.
Gale was replaced by Tommy Glidden, who was effectively shackled by Wednesday's left back Ted Catlin.
A West Brom attack broke down leaving Catlin injured, but the referee Bert Fogg played an advantage and a quick break saw Mark Hooper and Ronnie Starling combine to feed Jack Palethorpe, who hit a right foot shot into the corner of the goal.
Starling was prominent in Wednesday re-taking the lead on 70 minutes when his pass released Hooper, who beat two men before hitting a shot past Harold Pearson that went in off the post.
In the final minute, Pearson parried a Hooper shot and Rimmer knocked the ball home from close range for his second goal.