Coventry's seemingly relentless march towards the Premier League looked to be heading for a setback as the Baggies held off a confident start to go ahead when Heggebo turned the ball in at the near post from an excellent Mikey Johnston centre.
He wasted a glorious headed chance to make it 2-0 soon after but the Norwegian was soon celebrating again as he stretched to convert another Johnston cross to double the lead.
The Sky Blues were just as threatening, however with, Sakamoto causing problems and a fizzing Torp shot clipped the top of the bar, while Simms and Eccles also went close.
Molumby's red card four minutes after the interval left the Baggies unable to cope and, within 12 minutes, Simms' glancing header and Torp's seventh goal of the season following a half-cleared corner had put the hosts firmly on top.
Frank Lampard's side were unable to add to their 43 league goals this season but did not need a fourth to secure victory and give them an eight-point lead at the top of the table.
They are next in action away to Middlesbrough on Tuesday, while West Brom host Birmingham City in a big derby showdown the following evening.