McFadzean would pull one back at the right end, but it wasn't enough as the Sky Blues are now winless in their last four matches.
Story of the match
West Brom made a confident start, trying to keep the ball in the Coventry half of the field.
With ten minutes left in the first half, Coventry nearly equalized as Todd Kane was picked out on the left side of the penalty area, his cross hitting the boot of Kyle Bartley, the ball harmlessly bouncing away.
Two minutes from the interval, the visitors doubled their lead. Furlong's delivery across the six-yard box bounced off of a number of bodies, McFadzean's being the last before rolling in.
Just after the hour mark, Kane met Fankaty Dabo's center from the left, but he volleyed wide. At the other end, Moore comfortably saved from Grant.
Sheaf blazed over from 20 yards out and Furlong got in front of Dabo's goal-bound effort. McFadzean did head past Johnstone to cut the lead in half, but that proved to be nothing more than a consolation.
Man of the match: Taylor Gardner-Hickman
Making just his third start at senior level, he was impressive in an unfamiliar role. He had great attention to detail, bundles of energy and had an eye for passing.