Huth broke the deadlock in the third minute from a Riyad Mahrez free-kick and after Mahrez had netted a brilliant solo goal early in the first half, the German centre-back headed in his second goal from a corner on the hour.
Tottenham Hotspur, who host Watford later on Saturday, and Arsenal, who visit Bournemouth on Sunday, are both two points further back.
Leicester have now won three league games in a row and remain on course for the most improbable English title triumph since promoted Nottingham Forest won the league in 1977-78.
City, playing at home for the first time since Pep Guardiola was announced as the successor to manager Manuel Pellegrini, have now lost six league games this season - as many as when they last won the league in 2014.
City's Sergio Aguero scores a consolation goal late in the match. Photo: Getty
- Telegraph