Kelechi Iheanacho’s goalscoring substitute appearance was not enough to compensate for compatriot Wilfred Ndidi who gave away a penalty as Leicester suffered a 2-1 defeat to Alex Iwobi’s Everton at Goodison Park on Wednesday.
The defeat leaves Leicester still in search of a win since the restart.
The Foxes seemed a certainty for a top-three finish and Champions League football but two draws and a defeat means they could drop out of the top four completely with Chelsea set to overtake them with victory at West Ham in the late kickoff.
Fifth-placed Manchester United who travel to the King Power on the final day of the season are now three points behind the Foxes.
Everton, meanwhile, move up to eleventh, one point off the top half of the log after recording back to back wins.
Ndidi and Iwobi were on from the start for their respective sides but Everton were the more enterprising with Brazilian forward Richarlison putting the Toffees ahead after ten minutes.
It was 2-0 six minutes later when Gylfir Sigurdsson scored from the spot after VAR djudged Ndidi to have handled the ball in the area.
Rodgers rang the changes at halftime, changing the shape of the team with Iheanacho sent on to partner Jamie Vardy who is still in search of a 100th Premier League goal.
It took five minutes into the restart for the changes to bear fruit as Iheanacho found the back of the net for his first goal since the restart.
The Nigerian striker had a fantastic chance to level matters soon after but fired over the bar when well-placed.
Yerry Mina replaced Iwobi in the 70th minute as Carlo Ancelotti locked shop with Everton holding on for the win.
Elsewhere, Pierre-Emerick Aubamayang moved joint top of the scoring charts level with Jamie Vardy on nineteen goals with a brace as Arsenal pushed bottom club Norwich closer to the precipe.
The Gabon striker’s first goal was his fiftieth in the competition and he becomes the fastest player to reach that mark for the Gunners.
Granit Xhaka and a debut goal from Cedric Soares gave the Gunners a 4-0 victory at the Emirates to leave the visitors eight points from safety.
The Gunners move to within six points of European qualification with the victory.
Allan Saint-Maximin was in devastating form as Newcastle United battered Eddie Howe’s Bournemouth at the Vitality Stadium.
The Frenchman set up three of the visitors four goals against the hapless Cherries who appear in freefall and shot of confidence.
Despite their atrocious run of form, Howe’s side remain just one point from safety and could yet mount a miraculous recovery in their remaining six games.