Colin Cameron's penalty was enough to see off Burnley at the Ricoh Arena.
Stern John returned to the starting line-up to partner the in-form Dele Adebola up front for the first time since August. Leon McKenzie dropped onto the left hand side of midfield, with Clive Clarke slotting in at left-back in place of the suspended Marcus Hall.
City started well and in the first minute Richard Duffy found space down the right and cut past Jon Harley to deliver a dangerous cross which was flicked behind for a corner. Burnley then created their first meaningful attack in the sixth minute and Andy Marshall had to be alert to smother a close range effort from Steve Jones.
The game had petered out somewhat for a good 15 minutes but Jones forced Marshall into another save with 24 minutes on the clock, although the City shot stopper was equal to it.
But in the 31st minute the Sky Blues took the lead thanks to a Colin Cameron penalty. The referee took his time awarding the decision but decided that John McGreal had fouled Dele Adebola and the former Wolves man made not mistake, blasting his spotkick high into the left hand corner, sending Danny Coyne the wrong way.
There was an instant response from the visitors who put City under some severe pressure but McKenzie almost put the Sky Blues two clear when he forced Coyne to tip over his crossbar with a lofted effort from the right edge of the area.
The Clarets continued to test their hosts and Wade Elliott sent a low free-kick narrowly wide with five minutes to go in the first half. Burnley had enjoyed the majority of shots on goal in the opening period but failed to take any of them, while the Sky Blues had defended solidly and got a vital foothold going into the second 45.
Not long after the break Adebola forced a good stop from Coyne with a fierce low shot across the face of goal as City looked to extend their advantage.
McKenzie went closer still to making it 2-0 when he hit the crossbar with a fine curling shot and then sent a powerful header over from a Darren Currie cross. It was then Currie's turn to try his luck, but his shot after good work by Adebola - was easily gathered by Coyne.
Having not created too many opportunities in the first half, City were not guilty of wasting some excellent chances to put the game to bed. With just over 20 minutes to go Stern John shot wide when he should have at least hit the target from Adebola's pullback.
Robert Page was the next player to come close, forcing a brilliant fingertip save from Coyne with a strong far post header from Currie's corner.
With seven minutes remaining Stephen Hughes came on for Currie for his first slice of the action since losing the captain's armband.
In the 87th minute Kyle Lafferty caught the Sky Blues defence off guard but thankfully the excellent Marshall was equal to his shot to prevent an equaliser.
After a poor first half, the game picked up in the second and City could have won by a bigger margin. The result was the most important thing and with another superb defensive performance this was an excellent three points going into a hectic festive period.
Coventry: Marshall; Page; Ward; Doyle; Adebola; John; McKenzie (Kyle 90); Cameron; Duffy; Clarke; Currie (Hughes 83). Subs (not used): Birchall; Bischoff; Virgo
Booked: McKenzie (68)
Burnley: Coyne; Thomas; Harley; McGreal; Duff; O'Connor (Mahon 79); Jones; Elliott (Branch 76) ; McCann; Lafferty; Noel-Williams. Subs (not used): Sinclair; Hyde; Foster
Booked: O'Connor (7); McCann (57); Harley (64)
Referee: M Thorpe
Attendance: 18,362 (1,062)
