Leicester had started the game brightly enough but tellingly failed to test Burnley keeper Brian Jensen.
It was the under-worked Paul Henderson who was almost caught out early on by a 20-yard drive from Micah Hyde but City were soon back on the attack with Matty Fryatt rounding Jon Harley before crashing in a close range shot from a tight angle which Jensen blocked with his legs.
Thereafter the game belonged to Burnley save for a late flurry from the home side which failed to pay dividends.
Burnley burst into life just after the half-hour mark with Alan Mahon denied by the woodwork twice in as many minutes.
First his long-range drive cannoned off the underside of the bar and then the same player struck the crossbar again, this time with a 25-yard free kick with Paddy McCarthy scrambling to clear Hyde's follow-up effort off the line.
The Turf Moor men continued to flourish and in time added on at the end of the first half they broke through when Mahon whipped in a free kick with Gray taking full advantage of poor defending to guide home a smart header from seven yards.
City continued to labour after the restart and despite using a full complement of substitutions.
And it was Burnley who went closest to doubling their advantage on 70 minutes when Wade Elliott robbed Patrick Kisnorbo before finding man of the match Mahon whose eight-yard shot was deflected for a corner which came to nothing.
City's best attacking move of the night came close to the end when Fryatt swept the ball out to the right to substitute Josh Low who found fellow replacement Elvis Hammond whose shot was turned round the post for a corner by Jensen.
Iain Hume's half-cleared corner to fell from the debutant Low who was unlucky to see his well-struck drive bounce off the top of the bar.