Micky Adams was given a double boost as the defensive duo of Marcus Hall and Richard Shaw both returned to the starting 11.
As well as being able to call on Hall and Shaw, the City gaffer also welcomed back Welsh international Robert Page, who missed the defeat at Plymouth last time out through suspension, having collected five yellow cards.
In the middle of the park Dennis Wise started alongside Michael Doyle, and with the loss of Gary McSheffrey to a two-match suspension Andy Morrell filled in on the right flank.
The game started well for City and in the second minute Dele Adebola got away from his marker and sent a looping header onto the roof of the net with Brian Jensen struggling to make a save.
But Burnley soon found their stride and in the sixth minute, the Clarets broke through City's rearguard and Marton Fulop had to produce a good block from Chris McCann's powerful effort.
With the action flowing from end to end, the next decent opportunity presented itself to Andy Morrell after good work from Adebola but his goalbound shot was blocked by the head of Clarets left-back Jon Harley.
The Sky Blues also had strong claims for a penalty when Andy Whing went tumbling inside the area after a clumsy challenge by Harley but the referee was not interested.
Coventry continued to carve out the better chances and when Morrell did well to get a cross in from the right touchline, John got a glimpse of goal but pulled his shot wide of the target.
Although the first half was far from a classic encounter, City were not really getting the rub of the green and five minutes from the interval, Whing sent a low cross whistling through the six-yard box which somehow evaded everybody and went behind for a goal kick.
The second period started much as the first had finished with the Sky Blues dominating most of the play but finding the well-drilled Burnley defence tough to break down in the final third of the pitch.
But with 54 on the clock Micky Adams' men finally made the breakthrough with Dele Adebola stealing in at the far post to smash the ball past the helpless Brian Jensen.
Good work from Dennis Wise set-up Andy Morrell to header towards goal and it was the powerful Adebola who was on the spot to break the deadlock and give the Sky Blue Army something to sing about.
James Scowcroft was the next to go close five minutes later, his shot deflecting off the boot of a Burnley defender to send the ball spinning over the head of Jensen and wide for a City corner.
On the hour the Sky Blues went agonizingly close to doubling their advantage and possibly putting the game beyond the visitiors. Adebola made one of his trademark surges into the box before powering the ball into the body of Jensen.
The ball spun across the face of goal into the path of the lively Scowcroft who saw his goalbound effort saved on the line by the feet of the Burnley 'keeper.
Scowcroft then went even closer to getting on the scoresheet six minutes later as the impressive Jensen twice denied the former Leicester and Ipswich man from point-blank range as City continued to crank up the pressure on Steve Cotterill's side.
The Clarets' boss made his final two switches with 21 minutes remaining, bringing-on Gifton Noel-Williams and Kyle Lafferty in place of Wade Elliott and James O'Connor in a bid to find a way back into the game.
Michael Doyle was twice on the receiving end of bad challenges from firstly Chris McCann and then two minutes later Micah Hyde, as tempers threatened to boil over.
Dennis Wise and Frank Sinclair both went into the book along with McCann and Hyde after pushing and shoving sparked by the McCann challenge on Doyle.
With 82 on the clock it looked as if City might pay for their squandered chances as Michael Ricketts was able to control a long throw in the box but his scuffed shot failed to trouble Marton Fulop between-the-sticks.
Micky Adams waited until a minute from time to make his first change of the afternoon, replacing the tireless Stern John with Don Hutchison and City looked to hang onto the lead.
Burnley gave the Sky Blues a real fright deep into stoppage time when defender Frank Sinclair smashing a looping half-volley just over Fulop's bar. However, City hung on for another three points here at fortress Ricoh.
Coventry: Fulop; Whing; Hall; Page; Doyle; Adebola; Scowcroft; Morrell (Impey 90); John (Hutchison 89); Shaw; Wise. Subs (not used): Ince; Jorgensen; Hutchison; Impey; Thornton
Burnley: Jensen; Sinclair; Duff; O'Connor (Noel-Williams 69); Hyde; Branch (Karbasiyoon 39); Ricketts; Elliott (Lafferty 69); McCann; Spicer; Harley. Subs (not used): Crossley; Courtney.
Booked: Ricketts (31), McCann (73), Sinclair (73), Wise (73), Hyde (75).
Referee: E Ilderton
Attendance: 19,641
