Nobody tried harder to secure the win for Coyle than former City striker Ade Akinbiyi who struck a post in each half.
City started brightly and created early opportunities for Ivan Sproule following good work by Michael McIndoe and Darren Byfield.
Clarets goalkeeper Gabor Kiraly made a fine save to palm away a towering header from City skipper Jamie McCombe.
At the other end City goalkeeper Adriano Basso saved well from Kyle Lafferty and Jon Harley in quick succession.
Basso then made an even better save to deny Akinbiyi whilst Wade Elliott drove inches wide of the far post.
Burnley who were missing eight players through suspension and injury were forced to make a further change when central defender Clarke Carlisle limped off just before the half hour mark.
Akinbiyi twice came close to opening the scoring just before the interval, firstly striking the post with a shot and then forcing a save out of Basso after a quickly taken Robbie Blake free kick.
Akinbiyi had a further opportunity six minutes into the second half but after receiving a pass from Blake shot wide of the near post.
The only goal of the game arrived after 66 minutes when Vasko got on the end of a McIndoe free kick to claim all three points.
Just to prove that it was not going to be Akinbiyi's day the striker managed to beat Basso with a shot but saw it strike an upright.
And despite concerted pressure by the home side City held on with Basso making one more fine save to palm away a header from Lafferty.