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Just moments later, Yaya Toure was next to try his luck, though his effort from 25 yards out proved straightforward enough for the Foxes keeper.
Man City continued to turn the screw as the game went on, though Jeff Schlupp appeared to be taken down in the box by a Bony challenge, but the referee rejected the appeal.
Pellegrini's side picked up from where they left off after the restart, as Silva raced onto a neat ball from Navas before pulling back to the unmarked Bony, who scuffed his shot wide of the mark.
Just a free kick was given, however, with Kramaric picking himself up and sending his set piece into the side-netting.
Normal service resumed moments later, however, as Schwarzer had to be at his best to palm away a thumping Sergio Aguero header, and in the 69th minute, he tipped Toure's curling effort past the post.
However, Man City killed off the game two minutes from time when James Milner collected Toure's pass and skimmed Wes Morgan to tap home from close range.
The result puts the Etihad outfit five points behind Premier League leaders Chelsea - though the Blues have a game in hand - while Leicester continue to flounder at the bottom of the table.