Matthew Upson’s late own goal denied Premier League bottom club Leicester victory as Everton drew a fifth home game in a row.
Steven Naismith’s opener gave manager Roberto Martinez hope of a first home league win since December.
Sloppy defending allowed boyhood Everton fan David Nugent to equalise for Leicester, before Esteban Cambiasso put the visitors in front.
But Upson turned Christian Atsu’s cross into his own net with two minutes left.
Leicester’s spirited performance ended a run of four straight defeats, and will have given manager Nigel Person hope that they can avoid relegation, even though the draw leaves them four points from a position of safety.
Everton, so impressive in their 4-1 Europa League victory over BSC Young Boys on Thursday, have repeatedly failed to transfer high-quality European form to domestic competitions.
Romelu Lukaku, who scored a hat-trick in Switzerland, was unable to follow that up with a goal against Leicester, although he did get a flick to Atsu’s late cross before Upson got the scoring touch.
The Belgium international had myriad chances to add to his season’s tally of 13 goals, but sent the ball high over the bar from eight yards in the first half after Seamus Coleman had held off Upson to cut the ball back, lifted a clear second-half chance too high from a lovely James McCarthy flick, and had a goal-bound header blocked in the final minutes.
Everton team-mate Ross Barkley was guilty of a bad first-half miss of his own, with Aaron Lennon getting down the right to deliver a low cross, and the ball running loose to the England midfielder to clear the crossbar after Lukaku’s attempt had been blocked by Wes Morgan.
Jeff Schlupp, denied by a great John Stones block at the end of the first half, blazed wide early in the second period after Tim Howard had parried a Matty James shot into his path.
Instead, it was the home side who scored first, as Lukaku held up Darron Gibson’s pass for Naismith, who cut in on to his right foot and squeezed a shot past Morgan and Robert Huth, and just inside a stranded Mark Schwarzer’s post.
But Everton’s defensive vulnerability has hurt them time after time this season, and they conceded a soft equaliser as two Leicester substitutes combined within a minute of coming on.
Jamie Vardy got down the right to play in a low cross, and Nugent turned in the loose ball as Howard and Stones got into a mix-up at the near post.
The visitors were soon in front thanks to another Howard error, as the United States international keeper flapped at a Riyad Mahrez cross, and Vardy cut back for Cambiasso to drive in from 10 yards.
It looked as though Cambiasso would be the match winner, but Upson’s own goal ensured that Everton finish the weekend six points above the relegation zone.