Leicester's Jamie Vardy came close to scoring on eight minutes but, when through on goal, his shot hit a post.
Kevin De Bruyne forced a smart save from Kasper Schmeichel shortly after the break before Man City were awarded a penalty on the hour, when Dennis Praet deflected Ilkay Gundogan's shot with his arm.
Sergio Aguero saw his spot-kick saved by Schmeichel, the fourth penalty a City player has missed this season.
Pep Guardiola's side eventually made the breakthrough when Jesus, just on for Aguero, latched on to a pass from the marauding Riyad Mahrez to score.
The three points extends second-placed Man City's lead over Leicester to seven.
Leicester: 28 Feb v Norwich (A)
Man City: 8 Mar v Man Utd (A)