Stanley's three-game unbeaten run came to an end as Coventry's Bright Onobakhare scored the only goal at the Wham Stadium in a game of limited chances.
John Coleman gave goalkeeper Dimi Evtimov his full debut and brought in Sam Finley and Liam Gibson from the side which drew with Southend last weekend.
It was a lively opening minute with Sean McConville denied by Lee Burge in the opening seconds while Coventry's Tom Bayliss fired just wide from distance.
But after that clear-cut chances were hard to come by for both sides.
QPR loan frontman Paul Smyth was lively for the Reds and he got the ball in the box and turned but his effort was off-target.
Stanley looked the more dangerous in the early stages, Burge tipping over a Finley ball in.
The Reds limited Coventry but the visitors did break quickly at times with Stanley's defence able to clear the danger.
Smyth played a dangerous ball across the Coventry area but no one could get on the end of it while a McConville clipped free kick from 20 yards out on 40 minutes was just wide of the post.
Coventry pressed towards the end of the first half with two dangerous corners from Enobakhare but thankfully for the Reds they came to nothing.
The Sky Blues passed the ball around well after the restart and they opened the scoring on 60 minutes.
Enobakhare raced with the ball from around 30 yards out, evaded a number of challenges and fired past Evtimov.
John Coleman made a double change immediately after as he looked to get back in it with Scott Brown and Luke Armstrong replacing Sam Finley and Paul Smyth.
And Offrande Zanzala came on with 10 minutes to go as the Reds went all-out for the equaliser.
Coventry still threatened though and sub Luke Thomas forced a save from Evtimov from a tight angle on 82 minutes and the keeper denied Thomas superbly with his legs in injury time.
Stanley just couldn't test Burge and Coventry left the Wham Stadium with the three points.