City need another 11 points to win their third title in four years. The result sees Leicester remain in third place with eight matches remaining in the season.
City's bid to win an unprecedented Quadruple goes on as they meet Borussia Dortmund in the Champions League on Tuesday, take on Chelsea in the FA Cup semifinals before facing Tottenham in the EFL Cup final later this month.
Kevin De Bruyne also came close after 23 minutes but his free kick rattled the crossbar.
City continued to control the game and Riyad Mahrez's tame close-range effort was saved by Schmeichel.
On the stroke of half-time, Leicester thought they had taken the lead against the run of play but Jamie Vardy's goal was also ruled out for offside.
The visitors finally found the breakthrough after 58 minutes when Mendy reacted quickest to a loose ball inside the box and scored with a curling finish.
City doubled their lead after 74 minutes when Jesus finished off a nice team move involving De Bruyne and substitute Raheem Sterling.
After the game, Leicester coach Brendan Rodgers told reporters defender Caglar Soyuncu contracted the coronavirus while away playing for Turkey and he remains in his home country.
"He is good and feeling fine and we will go through the process seeing when he can be back," Rodgers said.
Soyuncu remains in isolation in Turkey following the World Cup qualifiers and Rodgers said it was "highly unlikely" he would be available for next Sunday's game at West Ham.
"The club is working with the Turkish federation to see where we're at," Rodgers said.
Information from the Associated Press was used in this report.