A solitary goal out of the Sky Blue from Coventry's Michael Doyle was enough to extend the Clarets' winless away run as Brian Laws' men drew a disappointing blank at the Ricoh Stadium.
A low-key game looked odds-on to run out a stalemate as the two sides increasingly cancelled each other out and found goal-scoring chances perilously difficult to chisel out.
The better ones fell Burnley's way but critically none were taken as the Clarets again failed to chalk up successive league wins for the first time this season.
And 12 minutes into the second half Doyle saw a chink of daylight to crack home his first goal in close to two years to send Burnley sliding back out of the play-off places as their five match unbeaten run on the road ground to a halt.
Despite the success of his substitutions as the Clarets got back to winning ways a week earlier, Laws had stuck with the same side that started against Watford.
And they repaid that faith by building a platform in an attritional opening half against a Coventry side looking to re-group after three straight defeats.
Jay Rodriguez fires in a free-kick
The Sky Blues were direct in their attempt to stop the rot with few frills in a no-nonsense approach which brought them an early opening when skipper Lee Carsley burst forward to let fly with a dipping shot which Lee Grant parried away.
When Burnley went route-one themslves they could have gone ahead after seven minutes when Grant pumped the ball forward for Jay Rodriguez to get clear in the box.
The Clarets' forward had just Kieren Westwood to beat but had to come in on the angle and the City keeper made a fine save as he stuck out an arm to block Rodriguez's left-footed shot.
Chris Eagles then fed in Chris Iwelumo but the top scorer delayed his shot and allowed Coventry defender James McPake to block.
The boss feels the frustration
The home side looked to get the ball forward early to strikers Marlon King and Clive Platt whenever the chance arose.
Clarke Carlisle and Michael Duff did a decent job of containing the pair, although when Carlisle was penalised for a foul on Gary McSheffrey, the winger picked himself up to fire in a top-corner bound free kick Grant superby saved at full stretch.
In a fiercely competitive opening 45 minutes both sides struggled to create clear-cut openings but Carlisle did put a heading chance over the top from a Graham Alexander corner while the Clarets looked capable of catching City on the break.
And when Eagles burst through the middle four minutes before the interval he was disappointed with the finish which saw him lift his shot tamely over the top after he had combined with Wade Elliott to part the City defence.
Michael Doyle puts Coventry ahead
The first goal always looked liable to be key and ten minutes into the second half Burnley had the opportunity to break the deadlock.
Tyrone Mears' ball over the top released Iwelumo but the big striker fired just wide from 18 yards.
And within two minutes the game had swung City's way as they went 1-0 up.
Wade Elliott almost levels
Burnley averted the immediate danger as Iwelumo did a good job of helping out his defence with a fine clearing header from Aron Gunnarsson's corner.
But the ball was retrieved by Doyle and from 25 yards he cracked a low left footer which fizzed through a crowd of players and beyond Grant's despairing dive.
Coventry-born Alexander replied with a long-range effort which bounced just wide but the real response came from Laws as he sent on Ross Wallace and Steven Thompson, who had sparked the comeback against Watford when they came off the bench.
As does Steven Thompson
This time the result was less spectacular as the Clarets couldn't find a route back into the game, although Thompson did get one sight of goal to try and rescue a point.
Rodriguez's charge through the middle committed defenders and Westwood and when the ball broke loose Elliott worked the space for a shot.
McPake got back to block and from the rebound Thompson sent his first-time volley inches wide as time ran out on another frustrating away day which brought the Clarets only a fourth defeat of the season.
Burnley: Grant, Mears, Easton, Carlisle, Duff, Alexander, Cork (Wallace 68), Elliott, Rodriguez, Iwelumo (Thompson 68), Eagles. Substitutes: Marney, Edgar, Bikey, Cort, Jensen.
Booked: Duff 62
Coventry: Westwood, Keogh, McPaike, Cameron, Wood, Baker (Gunnarsson 54), Carsley, Doyle, McSheffrey (Clarke 81), King (Jutkiewicz 74), Platt. Substitutes: Crainey, O'Donovan, Eastwood, Ireland.
Booked: McSheffrey 34, McPake 55
Referee: David Webb.
But the striker feels the pain of defeat