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.
Here are the RATINGS.