Matej Vydra opened the scoring in the fourth minute before Kelechi Iheanacho equalised half an hour later.
Sean Dyche’s men hit the woodwork and brought Kasper Schmeichel into some excellent saves as the scoreline remained at 1-1.
A draw extended the Clarets’ advantage over the bottom three to six points.
Here is how some Burnley fans reacted to the result on social media:
@BfcBlake7: I'll take it
@mattyh2602: Should have won by miles. Leicester’s keeper kept them in it today. Bring this style to Arsenal and 3 points easily.
@JoshChew96: Can't be upset with a point against a top team but our performance deserved more. Wood and Vydra absolutely ran the show.
@ConnorMartin224: Gladly take that. Wish we could play like that every week. Great performance.
@pye_luke: How haven't we won?
@BlokeFromCas: Could easily have had all three points. Much, much better than the past two games.
@short_antony: Much more like it, really enjoyable performance, just a pity we didn't get the 3 points. #twitterclarets
@JordanMayteee: Looked threatening every time we went forward. Chuffed for Vyds.
@jakehoskin16: Top drawer performance, not often a keeper pulls off a couple of worldies at the turf that isn’t Nick Pope. Gotta push on now #utc
@nathan_L20: Before the game, would have taken a point all day long so can’t be disappointed and the performance was so much better tonight!!
@Sam33084087: I'll take a point against a side in the top 4 anyday. Should have won it though