Everton grabbed the lead in the 10th minute when 19-year-old Anthony Gordon did well on the left, pulling the ball back and into the path of Brazilian Richarlison who slotted home.
Carlo Ancelotti’s side doubled their lead, in controversial circumstances, when Michael Keane and Wilfred Ndidi challenged for a header in the box and after a long VAR review, referee David Coote ruled the Leicester midfielder had handled the ball.
Gylfi Sigurdsson confidently converted from the spot and with his side 2-0 down at the break, Leicester manager Brendan Rodgers made a double change with James Maddison and Kelechi Iheanacho introduced.
The switch had a swift impact with the visitors pulling one back six minutes after the restart, when Jamie Vardy caused panic in the Everton box, Iheanacho sought the loose ball and Mason Holgate’s clearance hit him and flew past Jordan Pickford.
England keeper Pickford then survived a scare when he fumbled a low cross from Marc Albrighton but Keane was alert to clear the ball off the line.
Leicester stayed on 55 points, one more than fourth-placed Chelsea who play West Ham United later on Wednesday.
Everton moved up to 11th on 44 points.
(Reporting by Simon Evans, editing by Ed Osmond)