The Merseysiders had taken the lead at Leicester's training ground through a Fraser Hornby solo goal, assisted by Harry Charsley.
Bolasie came on for his first appearance since last December on 61 minutes but Leicester won it late with two goals in the final six minutes from centre-back Yohan Benalouane.
The Foxes are up to second, two places and four points above defending Division 1 champions Everton, for whom David Unsworth was back in charge.
Leicester: 14 Dec v Legia Warsaw (H) PL International Cup
Everton: 15 Dec v Dinamo Zagreb (H) PL International Cup