Albion hit the home team - who had Michael Doyle sent off at the start of the second half - for five and they could have had even more as they turned on the style against their woeful West Midlands rivals.
New Sky Blues' signings Dan Fox and Scott Dann were cup-tied and caretaker boss Frankie Bunn brought Marcus Hall and Arjan De Zeeuw into the backline.
West Brom were without the suspended Jonathan Greening and drafted Zoltan Gera and Roman Bednar into attack.
The visitors had the better of the opening exchanges and teasing crosses from both wings found the City defence flat-footed.
It was no surprise when a quick throw-in from West Brom after 12 minutes allowed Bednar to cross from the right which was headed powerfully home by Chris Brunt from five yards.
It seemed Coventry were caught offside almost every time they attacked the Baggies goal, with lone striker Leon Best the biggest culprit.
However, despite being out-muscled by West Brom, the Sky Blues improved after going behind and created several chances.
Best headed the home team's clearest chance of the half over the bar in the 34th minute following a pinpoint cross from City left-back Hall.
Shortly after the restart, the Sky Blues gave themselves an uphill task when captain Doyle was red-carded for a dangerous challenge on Gera.
A West Brom victory was all but sealed on 59 minutes when city keeper Andy Marshall gifted his clearance to Bednar, who made it 2-0 when he stroked the ball into the back of the net.
Worse was to come for Coventry when a Bednar chip into the box was handled by de Zeeuw.
The resulting penalty was blasted to right of Marshall by Bednar for his second goal of the afternoon.
A miserable afternoon for the hosts was capped with two late goals in two late minutes from substitute Ishmael Miller and Gera.