Leicester looked set to register their fifth win of the season when David Nugent and Esteban Cambiasso put them 2-1 up after Steven Naismith had broken the deadlock.
But with less than two minutes left Christian Atsu crossed for Romelu Lukaku, whose diving header flew past Mark Schwarzer after taking a huge deflection off Matthew Upson and the match ended 2-2.
Lukaku had looked a shadow of the man that bagged a hat-trick against Young Boys on Thursday.
The Belgian missed several chances against the Foxes, but he was in the right place at the right time to grab a point for Roberto Martinez's team although he will be grateful to Upson for deflecting the ball in.
Lukaku was not the only poor performer for the hosts on Sunday
Everton were poor all over the pitch and can count themselves lucky to claim a point.
Ross Barkley was hooked after 53 minutes following a poor display and Aaron Lennon quickly faded after a bright start
Tim Howard was also poor
The American goalkeeper gave his critics further ammunition by flapping at two crosses, which allowed the Premier League's bottom club to score twice.
Nigel Pearson will be bitterly disappointed not to take all three points from his trip to Merseyside, but he can take heart from the fact that his team are now four points closer to safety, rather than five.
Everton took a while to get going in Switzerland on Thursday and it was much the same case at Goodison Park as Leicester started strongly.
Jeffrey Schlupp was their most dangerous player in the opening stages, firing a low drive at Howard.
Schlupp burst into the box moments later and it needed the combined efforts of three Everton players to stop the Ghanaian.
The home fans were unhappy as Everton lacked any pace or purpose going forward
They briefly woke from their slumber when Lukaku collected and went clean through following an incisive pass by Barkley, but the striker was offside.
Everton wasted the few chances they had in the first half
Barkley curled a 20-yard free-kick into the Park End and Lukaku did the same moments later.
Andrej Kramaric came close at the other end when he curled his shot a foot over Howard's goal.
John Stones then put in a last-ditch block to deny Schlupp in first half injury time.
The game was a far more entertaining affair in the second half
Just two minutes after the break, Howard parried Matty James' shot, but Schlupp dragged the follow-up wide.
Boos rang out around Goodison Park in the 53rd minute when Muhamed Besic, who had controlled the game from midfield was replaced by Atsu
Darron Gibson came on for Barkley, who had been far less effective.
Any dissenting voices were muted four minutes later when Everton took the lead
Lukaku held the ball up brilliantly and laid the ball off to Naismith, who squeezed his shot between Wes Morgan and Robert Huth and the ball trickled past Mark Schwarzer.
Pearson made a double change, bringing Nugent and Jamie Vardy on.
Just over one minute later, the pair combined to equalise
Vardy pulled away down the right and drove a low shot goalwards which Howard spilled straight into the path of Everton fan Nugent, who tapped in.
Lukaku should have put Everton back in front when he meandered through the Leicester defence, but he somehow contrived to clear the bar from 10 yards.
The hosts were punished immediately by the Foxes
Howard was at fault again
He flapped at a cross and Vardy pulled the ball back to Cambiasso, who drilled the ball in from inside the box.
The Everton fans groaned as Lukaku wasted yet another chance to score as the former Chelsea striker could only muster a weak shot after being played in by Naismith.
The Belgian made a telling impact in the dying minutes, though, when his diving header hit Upson and flew in to steal a fortuitous point for Martinez's side.
Source : PA
Source: PA