The Gas exit the Emirates FA Cup at the Third Round stage at St Andrew’s.
Biamou’s neat finish inside the opening five minutes game gave the home side an early advantage in the contest.
Rovers had chances of their own as the first-half played out, the clearest attempt coming midway through the opening 45 minutes, as Clarke-Harris clattered the crossbar with a powerful header.
In the second half, the Sky Blues grasped the all-important second goal through a powerful finish from Josh Pask, with Biamou grabbing a third goal from close-range just moments later to complete the scoring and to knock Rovers out of the competition.
Ahead of the tie, Rovers made one change to the side that faced Doncaster on the weekend prior.
The change saw Josh Barrett, who was ineligible for the tie, drop out of the starting XI. The playmaker was replaced by Tareiq Holmes-Dennis, who was deployed in a role that saw him operate further up the pitch, in a more attacking capacity.
In the early stages, there were anxious moments for Rovers, as a low effort from Josh Pask forced a save from van Stappershoef. The Rovers ‘keeper was able to take the sting out of the effort and pounce on the loose ball at the second time of asking.
Rovers didn’t take warning from the early endeavours from the home side, as the host’s grabbed the game’s opening goal in the 4th minute.
It was O’Hare’s through ball that played Biamou through on goal and he made no mistake in placing a finish beyond van Stappershoef, slipping a side-footed finish inside the far corner.
Both sides tussled for possession as the first-half progressed, with Rovers aware of the focus on the home side to break forward at pace when the opportunity presented itself.
In terms of chances, Coventry came close to threatening the Rovers goal when Pask’s sweeping low cross narrowly missing Biamou at the back post, as the goal scorer slide in to touch the cross home.
Rovers responded well and fashioned two chances in quick succession, both coming via the combination of Luke Leahy and Jonson Clarke-Harris.
Leahy’s cross from wide out on the left flew high into the congested penalty area, with the striker managing to direct a header onto the crossbar.
An exact copy of the delivery moments later from Leahy again reached the striker, who this time was able to leap higher off the ground to meet the cross, but directed a powerful header high over the target.
With Rovers creating more attacking play, they still had to be alert at the back, as the home side carried a threat throughout the first half. A searching corner from Jamie Allen reached the head of Dom Hyam, who guided a glancing header towards the target that was cleared off the line by Clarke-Harris, in what was an important interference to keep the deficit the one-goal.
In the final stages of the first half action, Liam Kelly curled an attempt from well outside the area high and wide of goal, as the one-goal advantage to the Sky Blues held into the interval.
At half-time, Holmes-Dennis made way for Victor Adeboyejo, as the Gas changed shape in order to offer more support to Clarke-Harris in attack.
It was Coventry who mounted the first goalmouth action of the second half, just minutes after the restart.
Skipper Kelly was able to feed the ball through to Jamie Allen, who shifted a low effort across goal that scampered just wide of the goalframe, taking a deflection in the process. From the corner that followed, Hyam directed a header harmlessly wide of goal, after throwing himself to the ground in a tussle with a Rovers defender.
The next goal of the contest was always going to be key and unluckily for Rovers, it fell the way of Coventry in just over five minutes after the break.
As with the first goal, it was a pinpoint pass from O’Hare that did the damage, as Pask was played in on goal and a powerful finish left little van Stappershoef could do to keep out the effort.
Just as Rovers restarted from Pask’s goal, the host were able to add a third.
It was a short corner that found Liam Walsh that created the opening, who looked to have no options available with a swarm of navy shirts blocking his sight on goal, but the midfielder blasted a low shot across goal that deflected off Biamou and into the net for the home side to take a three-goal lead.
In the remaining 30 minutes, the home side seemed content to protect their lead and limited any venture into their penalty area. Menayese had a tame effort comfortably stopped by Marosi, as the defender miscued a volley from the edge of the box.
Clarke-Harris shortly after tested the Coventry ‘keeper with a powerfully struck free-kick that kept low and swerved around the wall, but Marosi was able to get a strong hand to the effort to push it wide of the target.
In the final ten minutes, Ollie Clarke replaced Ed Upson, marking a return from injury for the midfielder.
The home side managed their lead and recorded the win to set up a tie at home against Birmingham City in the next stage of the competition.
Rovers are back on the road on Saturday, as they travel to face Rotherham United.
Coventry City: Marko Marosi (G), Michael Rose, Brandon Mason, Kyle McFadzean (84' Jordan Shipley), Liam Kelly (C), Jamie Allen, Max Biamou, Dom Hyam, Josh Pask, Callum O'Hare (60' Jodi Jones), Liam Walsh
Subs: Ben Wilson, Jordy Hiwula, Amadou Bakayoko, Declan Drysdale, Josh Eccles.
Bristol Rovers: Jordi van Stappershoef (GK), Tareiq Holmes-Dennis (45' Victor Adeboyejo), Cameron Hargreaves (62' Michael Kelly), Tony Craig (C), Ed Upson (83' Ollie Clarke), Liam Sercombe, Jonson Clarke-Harris, Luke Leahy, Alfie Kilgour, Rollin Menayese, Alex Rodman.
Subs: Alexis Andre-Jr (GK), Kyle Bennett, Tom Davies, Tom Nichols.