In their first match since Florida-based entrepreneur Shilen Patel formally completed his takeover of the club on Wednesday, goals before halftime at The Hawthorns from Mikey Johnston and Grady Diangana put the Baggies on the road to victory.
Haji Wright pulled a goal back for Coventry with a penalty 17 minutes from time to give the visitors renewed hope of a draw.
The win left the fifth-placed Baggies seven points clear of Norwich, in seventh spot, with Coventry remaining in ninth – four points adrift of the play-offs.
"I'm enjoying myself and my football right now," Johnston, on loan from Scottish champions Celtic, told Sky Sports.
"The win was important. I just hit the target. We need to get wins and just stay up there," the winger added.
It took the Baggies just six minutes to open the scoring with Johnston beating two defenders on his way into the box before curling an excellent shot into the far corner.
Both Midlands clubs had chances to score before West Brom doubled their lead nine minutes before the break when Diangana turned in Tom Fellows's fine cross.
Coventry, however, pulled a goal back in the 73rd minute, when Wright scored from the spot after Cedric Kipre brought down Kasey Palmer.
Championship leaders Leicester are currently six points clear at the top of the table, while second-placed Leeds are level on points with Ipswich in third.