For Burnley it marked the end of a mini-revival which had seen them unbeaten in four previous games.
Patrick Suffo scored a fine opportunist goal to give Coventry the lead in the eighth minute and the match was effectively out of Burnley's reach when Paul Weller headed past his own goalkeeper in spectacular style on the half-hour.
It was a bizarre scoreline in a game the home side had dominated - Burnley had forced 11 corners before Coventry managed one.
It seemed that Burnley's pressure must eventually produce a reward and it did seven minutes after the break when Robbie Blake scored for the 12th time this season with a clever shot from the edge of the box.
The Clarets would have won a point but for a glaring miss by Mo Camara who somehow managed to shoot wide with the goal gaping just six yards out.
Burnley's miserable afternoon was completed when French defender Arthur Gnohere was sent off in stoppage time for the second of two yellow card offences.
Burnley boss Stan Ternent said: "It was disappointing to lose, as ever, but we conceded a very poor first goal and an even worse second one.
"We were much better in the second half but had given ourselves too much to do."
Coventry's stand-in manager Eric Black said: "It's not been an easy few days but the players responded magnificently and this is a big win against a very good side.
"We had some great defensive performances and although Burnley had a lot of pressure, they didn't get too many sights at our goal."