With a quarter of the game gone, Liverpool looked to be cruising to victory after Coutinho curled a free kick beyond the despairing dive of Schmeichel.
Leicester thought they had pulled a goal back five minutes before the break after a set-piece saw Harry Maguire feed the ball into Shinji Okazaki to slot past Simon Mignolet, only for the offside flag to go up.
However, the Foxes were back on terms in first-half injury time as Okazaki prodded the ball into the net from very close range. Liverpool players immediately surrounded referee Anthony Taylor, enraged by the decision not to award a foul in the build-up, but the goal stood.
Leicester, however, had other ideas and immediately hit back through Jamie Vardy's header, and the Foxes were then awarded a penalty after Mignolet was adjudged to have fouled the England forward on the edge of the box.
The Belgian keeper, shown only a yellow card despite appearing to be the last man, duly saved Vardy's kick.
Leicester thought they had another shout for a penalty when Can appeared to handle the ball, only for the referee to wave away the appeals.