The Midlands side were 3-0 up by the break as they steamrollered a Wednesday team who are without a win in six games leaving them three points off the drop-zone.
The Sheffield side were in trouble in the opening minutes as they failed to clear Luke Moore's teasing ball into the area and former Wednesday midfielder Chris Brunt stretched to fire in a header which was tipped over the target by Lee Grant.
Wednesday, over-run in midfield and struggling to contain the Midlands side's cultured approach work, finally came unstuck in the 23rd minute.
Graham Dorrans' corner should have caused no problems but the Sheffield rearguard was slow to react as Simon Cox struck from six yards, his fourth of the season.
West Brom added a second in the 30th minute. Brunt's low cross from the left was touched on by Moore as Lewis Buxton failed to intervene and Cox finished clinically from ten yards.
Moore squandered a chance firing over the target as Wednesday fell apart. They escaped when full-back Tommy Spurr sent Cox sprawling in the area before West Brom increased their lead, Thomas and Cox cleverly linking before Thomas added the finish touch with a low shot into the right-hand corner.
All Wednesday could produce in reply were long-range strikes from Marcus Tudgay and James O'Connor which were both dealt with comfortably by Scott Carson.
Moore threaded the ball through the Wednesday defence again on 56 minutes as West Brom were not content to sit on their lead.
He weaved his way past two defenders before finishing with a low right-foot strike from 15 yards, the ball flashing wide of the far post as the overworked Lee Grant scrambled across his line.
Cox turned quickly to fire narrowly over the target from 16 yards before the impressive Brunt added a fourth, substitute Chris Wood picking out the winger who fired home from ten yards for his sixth of the season.