Forward Gayle – who had already netted three times since joining Darren Moore’s side on loan until the end of the season – had a hand in his team’s opener at the Hawthorns as he was brought down in the box by Adam Webster, with Jay Rodriguez stepping up to convert the spot-kick.
Gayle then bagged his fourth goal of the campaign on 24 minutes, sweeping home to make it 2-0, before another Rodriguez effort four minutes later made it three.
Lloyd Kelly pulled one back for the Robins before Harvey Barnes put the result beyond doubt with a fine strike, rendering Famara Diedhou’s consolation worthless.
Twenty-seven-year-old frontman Gayle was replaced by Wes Hoolahan with quarter of an hour left on the clock.
The result lifts Moore’s men up to third in the Championship table, and they are now just four points shy of leaders Leeds.
Elsewhere in the Championship, Jack Colback could feature for Nottingham Forest when they entertain Sheffield Wednesday on Wednesday night.