Matej Vydra gave the Clarets the ideal start when scoring his first league goal of the campaign.
The striker pounced on Hamza Choudhury's error, took the ball past Wilfred Ndidi before beating Kasper Schmeichel with an emphatic finish.
The Foxes equalised in the 34th minute when Kelechi Iheanacho hit Ndidi's pass over the top first time to beat Nick Pope.
Both sides had chances to win it with Schmeichel clawing James Tarkowski's header off the line before the break and then producing a wonderful fingertip save to keep out Chris Wood in the second half.
Ashley Westwood also saw his volley come back off the upright while Youri Tielemans was denied by the woodwork at the other end.
5. Ben Mee 6.7
Took some time to get to grips with Iheanacho's movement, losing the Leicester striker a couple of times in the first half, including for the equaliser. Dominant in the air when the visitors swung the ball into the box from wide areas.
6. Josh Brownhill 6.5
Didn't contribute a great deal in the final third, but stuck to his defensive duties admirably, pinning the lively Castagne back. Whipped a well-placed set-piece over the bar in the second half.
7. Dwight McNeil 6.6
Looked much more lively. On his toes to intercept the ball in Leicester's attempts to switch the play while his deliveries - both from set-pieces and in open play - were much improved. Still needs to step it up another gear.
8. Ashley Westwood 7
Another strong box-to-box display from the midfielder, who is able to knit the play together in both halves of the pitch. An energetic display and unfortunate to see his well-struck volley come back off the post.