A second-half strike from Dele Adebola was enough to secure the points for Coventry as Burnley goalkeeper Brian Jensen performed heroics to keep the score down.
Adebola struck in the 54th minute but Jensen was at his best to deny the striker again soon after to keep the Clarets in with a chance of rescuing a point.
Jensen also saved well from James Scowcroft as the home side pressed for a second goal to make the game safe.
Burnley had won only once in their last eight games and have not recorded a victory on their travels since their 3-2 triumph over Luton back in November.
While the home side's away form has also been disappointing of late, the Sky Blues have enjoyed far more success at the Ricoh Arena with four straight league wins.
And they made a bright start as Adebola sent his header over the bar with just over a minute gone.
But the visitors were denied the chance to open the scoring four minutes later when Chris McCann's left-foot effort forced Marton Fulop into a superb save.
Dennis Wise, back in the side after coming off the bench to score in the 3-1 defeat at Plymouth, curled a free-kick wide in the 17th minute.
Stern John wasted a decent chance nine minutes later when he managed to get onto a Andy Morrell cross, only to send his shot wide.
Scowcroft headed over from Wise's corner before the former Chelsea captain forced Brian Jensen into a wonderful save from his 36th-minute in-swinger.
And just before the break, Wade Elliott's curled effort from 20 yards was caught by Fulop while John headed wide from close range.
Coventry went ahead nine minutes into the second half when Wise's header was pounced upon by Adebola and the former Birmingham striker tucked the ball into the back of the net for his ninth goal of the season.
And only the heroics of Jensen on the hour mark denied Adebola a second when the Danish goalkeeper pulled off a fantastic close-range save before immediately denying the lurking Scowcroft.
The Sky Blues continued to lay siege to the Burnley goal and Scowcroft smashed a shot against the post in the 67th minute before Jensen was again at his best to deny the former Ipswich man.
McCann, Frank Sinclair and Wise were all booked following a bad foul by McCann on Michael Doyle in the 71st minute as the visitors' frustrations started to bubble over.
Michael Ricketts saw his shot gathered by Fulop as the game entered the final 10 minutes while Sinclair fired over the bar as Coventry held out for the win.
Teams
Coventry Fulop, Whing, Page, Shaw, Hall, Morrell (Impey 90),Wise, Doyle, Scowcroft, Adebola, John (Hutchison 89).
Subs Not Used: Ince, Jorgensen, Thornton.
Booked: Wise.
Goals: Adebola 54.
Burnley Jensen, Elliott (Lafferty 69), Sinclair, Duff, Harley,Spicer, McCann, James O'Connor (Noel-Williams 69), Hyde,Branch (Karbassiyoon 39), Ricketts.
Subs Not Used: Crossley, Courtney.
Booked: Ricketts, McCann, Sinclair, Hyde.
Att: 19,641
Ref: E Ilderton (Tyne & Wear).