Leicester are headed in the opposite direction as their winless run since English football’s restart from the coronavirus pandemic stretched to four games.
Richarlison and Gylfi Sigurdsson’s penalty gave Everton the perfect start at Goodison Park.
Toffees are yet to lose at home under Carlo Ancelotti and they held on in the second half for a vital three points for their own ambitions of European football next season.
Kelechi Iheanacho’s fortunate goal as the ball ricocheted in off his face reduced Leicester’s arrears and they pressed hard for an equaliser in the closing stages.
Michael Keane’s clearance off the line spared Jordan Pickford’s blushes after another huge error from the England number one.
However, defeat means Leicester could drop to fourth should Chelsea win at West Ham later on Wednesday and the Foxes are now just three points clear of Manchester United and Wolves in the battle for a place in the Champions League next season.
At the bottom of the table, Bournemouth also suffered a huge blow in their battle to beat the drop with a humiliating 4-1 home defeat by Newcastle.
Dwight Gayle, Sean Longstaff, Miguel Almiron and Valentino Lozaro were on target for the Magpies, who were not distracted by the ongoing uncertainty around the club over a proposed Saudi takeover.
Bournemouth remain in the bottom three and the margin of defeat could also prove costly as they drop below Aston Villa on goal difference into 19th.