Leicester moved level on points with Premier League leaders Arsenal as they held title rivals Manchester City.
Raheem Sterling drew three saves from Kasper Schmeichel in the first half, but Leicester's Jamie Vardy had the best chance, firing over from 18 yards.
Sergio Aguero turned over from close range after the break before looking frustrated when he was substituted.
The visitors, who saw more of the ball, had 21 shots on the night but Leicester defended admirably to earn a point.