Caretaker boss Michael Appelton made eight changes for the game as he tried to keep his squad fresh just days after their win over Swansea City in the Premier League.
Leeds manager Thomas Christiansen also made alterations, with 10 players coming into the starting XI on Tuesday night. Jay-Rot Grot had the first opening of the game but he was denied at the near post by Leicester stopper Ben Hamer.
Leeds' Kemar Roofe also went close in the 14th minute before the Whites opened the scoring through Pablo Hernandez. The former Swansea man was given too much space before curling the ball into the top corner.
Leicester pulled a goal back just three minutes later, as Iheanacho scored his first goal for the club after capitalising on an error at the back from Leeds.
Appleton had to wait until the 71st minute before his side went in front, with Slimani volleying home just minutes after he wasted a glorious chance from close range.
Mahrez was thrown on from the bench and he did his job within minutes as he dribbled past several players before curling the ball into the bottom corner to send Leicester through to the next round.