Richarlison and Gylfi Sigurdsson struck early on as Leicester's grip on a Champions League place was loosened yet further with defeat at Goodison Park.
Kelechi Iheanacho gave the Foxes hope of arresting their damaging recent slump with a bizarre goal, but Everton held on for three Premier League points.
Brendan Rodgers' side, third going into the game, have now not won in three since the league resumed and a fine season is in danger of fizzling out as the chasing pack close in.
Everton took a firm grip after just 10 minutes. Anthony Gordon raced onto a header from Lucas Digne down the left and squared the ball for the onrushing Richarlison who made no mistake.
Everton doubled their lead with just 16 minutes gone when VAR awarded them a penalty. Digne swung the ball into the box and it appeared to strike the arm of Wilfred Ndidi as he got ahead of Michael Keane. Sigurdsson stroked home calmly from the spot.
Substitute Iheanacho got lucky but was rewarded for his persistence as he chased a ball into the box and Mason Holgate's attempted clearance struck him on the head and went in.