Only a last-gasp goalline clearance denied Rovers a deserved point as their comeback fell just short at the Ricoh Arena.
The Sky Blues struck twice in a decisive 20-minute spell in the opening half through Jordy Hiwula and Luke Thomas and, although Rovers fought back to control the second period, they could only pull one back through Joe Wright’s second goal of the season.
They piled on the pressure in the second period, with the late stop from John Marquis’ shot at the end of four minutes of stoppage time ultimately ensuring the home side came away victorious.
Grant McCann was forced into making two changes from Tuesday’s game against Sunderland, with Andy Butler and Niall Mason dropping out due to suspension. Tom Anderson and Ali Crawford came into the side in place of the suspended pair, with Matty Blair switch to right-back.
The first chance of the half fell to the hosts as Coventry captain Michael Doyle took aim on the Rovers goal, his shot was deflected into the air and had to be tipped over the crossbar by the alert Marko Marosi.
Rovers had their first half-chance of the game in the 13th minute when a James Coppinger corner found the head of Wright who was up from the back, but his effort only found the hands of Burge in the Sky Blues goal.
Mark Robins’ outfit continued to press and two minutes later they went close to opening the scorning when a free-kick from Doyle was headed goalwards by Tom Davies, but Marosi was there to make another save to keep the scores level.
McCann’s side were threatening from corners and should have been one goal to the good through Anderson after Coppinger’s delivery was met by the centre-back, who was unmarked, but he could only head his effort over the bar.
Coventry took the lead in the 21st minute as another Doyle free-kick tested the Rovers defence. It was initially cleared by the back-line, but only as far as Jordy Hiwula who smashed his left-footed volley past Marosi in the Rovers goal.
The home side nearly doubled their lead 14 minutes later when a corner was only half-cleared by the visiting defence, the ball was picked up by Jordan Willis who only found the Rovers fans behind the goal with his attempt.
Former Rovers loanee Jonson Clarke-Harris was the next to try his luck - he did well to beat Blair for pace, but dragged his left-footed effort wide of the mark.
The Sky Blues did make it 2-0 with five minutes of the first period remaining when Luke Thomas took aim from 20-yards out and found the back of Marosi’s goal via the inside of the right-post.
Rovers had the first chance of the second-half and it came from an in-swinging deliver from Andrew. his sweetly struck set-piece just needed a touch at the back post, but nobody was there to apply the finishing touch.
McCann rolled the dice in the 57th minute with the introduction of Peterborough United loanee Jermaine Anderson and Paul Taylor, which saw Crawford and Mallik Wilks depart the field of play.
It paid off in the 69th minute when a well-worked move saw Coppinger fire his cross into the path of substitute Taylor, who laid the ball off perfectly for Wright who fired home his second of the campaign.
Rovers pushed for a equaliser and with three minutes of normal time remaining Rovers were inches away from claiming a point.
A drilled cross from Andrew was picked up by Blair whose shot was blocked before it fell to Whiteman on the half-volley, but his effort went wide of Burge’s goal.
Rovers continued to press the Sky Blues back into their own half late on, and they came close to claiming a deserved point in the final minute of additional time.
A powerful run into the box from Andrew saw his cross fired at goal by Marquis, but Burge and a defender did brilliantly to force the ball away to safety and preserve victory for the home side.