An equalising goal 12 minutes from time by Foxes striker Iain Hume earned Ian Holloway's side a share of the spoils at Turf Moor and maintained their impressive form away from home.
Burnley striker Robbie Blake was the architect of many of the best opportunities that the Clarets created in the opening half. None more so when he got on the end of a move involving Graham Alexander and Wade Elliott only to see his shot deflected away for a corner.
But the home side did not have to wait long before going in front as, from the resultant corner taken by Blake, the ball was returned to the Burnley playmaker.
He eased his way to the byline and pulled the ball back for central defender David Unsworth to score his first goal for the Lancashire side with a sweet left-foot finish.
A swift counter-attack involving Andy Gray and Alan Mahon was carried on by Blake who this time saw his shot blocked.
A Blake corner was headed over by Chris McCann while another Blake pass created an opportunity for Kyle Lafferty but he shot wide of the target.
After withstanding that spell of pressure, Leicester created a couple of chances with Richard Stearman heading over and Stephen Clemence shooting wide.
The half finished however with Burnley creating further opportunities as Blake slipped with only keeper Marton Fulop to beat and Mahon blasted wide on the stroke of half-time.
The home side continued to make the running at the start of the second half with Fulop saving from Gray and Lafferty again shooting wide.
Lafferty continued to try his luck in front of goal and a shot from the teenage striker was spilled by Fulop as far as McCann whose shot was cleared off the line by Patrick Kisnorbo.
Holloway made a double substitution with 20 minutes remaining replacing Alan Maybury and Alan Sheehan with Andy King and Ashley Chambers.
King was involved in the move which led to the equalising goal as his pass found Stearman who crossed for Hume to score.
But the home side continued to press for a late winner with leading goalscorer Gray seeing his shot saved by Fulop after a teasing throughball from Mahon and Lafferty missing the target after some excellent approach play.
The home side created one last opportunity in stoppage time as a header from central defender Clarke Carlisle was cleared off the line by Leicester skipper Clemence.