Aston Villa threw away a two-goal lead as Marouane Fellaini's second of the match deep into added time denied the visitors a much-needed Premier League win at Goodison Park.
For a long time it appeared Paul Lambert's side would be celebrating their second surprise success on Merseyside, having beaten Liverpool in December.
But Fellaini scored his second of the afternoon to add to Victor Anichebe's first-half strike and cancel out Christian Benteke's double and a goal from Gabriel Agbonlahor.
Everton's remarkable powers of recovery came to the fore again and they are second only to Manchester United having taken 21 points from losing positions this season, although the draw was not enough to take them back into the top four for the first time since December 22.
It was a huge blow to Villa, who since their last league success at Anfield seven weeks ago - which in itself was something of a surprise - have now picked up just three points.
Lambert's side arrived in the north-west in much worse form than when they turned over Liverpool and, although they left with a point, they will be disappointed.
Everton had shown in the midweek 2-1 win over West Brom - another side in a poor run of form - that their defence was not entirely watertight, but conceding in the second minute lead was disappointing even for them.
John Heitinga, whose defending could best be described as haphazard, was completely culpable as Benteke went past him as if he were standing still - which he may as well have been - to slide a shot across Tim Howard from Charles N'Zogbia's pass.
Fellaini almost produced an instant response, rolling a shot just wide of Brad Guzan's right post before Anichebe had an effort patted down by the American.
Benteke continued to look threatening, however, and his shot from Agbonlahor's cutback was deflected behind before Everton drew level thanks to their own powerhouse forward.
Anichebe was again preferred up front to Nikica Jelavic, and he repaid manager David Moyes' faith with a 21st-minute equaliser.
Having held up Kevin Mirallas' pass by using his superior upper body strength, he then turned Ciaran Clark to fire a left-footed shot past Guzan for his fifth goal in eight league starts.
Both sides looked weak defensively and Heitinga, who has not enjoyed the best of seasons, was again involved in Villa's second.
A corner was only partially cleared and Ashley Westwood's right-wing cross saw Agbonlahor lose the Holland international and outjump Fellaini to head in at the far post.
Heitinga's afternoon failed to get any better after the break as he went to head the ball and succeeded only in connecting with team-mate Phil Jagielka - the player moved out of his best position in central defence to accommodate the Dutchman.
Fellaini received an even more painful blow when he collided with Guzan trying to reach Leighton Baines' inswinging free-kick and, although he returned, his movement was restricted.
Villa should have put the result to bed soon after when Agbonlahor played in Andreas Weimann, but the Austrian blazed well over with only Howard to beat.
He made up for it with his involvement in the third goal, which saw him exchange passes with Matthew Lowton, allowing the right-back to curl in an inviting cross to which Benteke beat Heitinga to nod in at the near post and take his Premier League tally into double figures.
The Dutchman was put out of his misery when he was replaced by Bryan Oviedo soon after with Jelavic coming on for Mirallas, who has yet to find his early-season spark after a niggling hamstring injury.
Some home fans booed Mirallas' departure - more did so Heitinga's for different reasons - but the change had the desired effect with 20 minutes to go.
Fellaini cut in from the left and again utilised Anichebe's strength to hold up the ball before taking the return pass to shoot past Guzan with the help of a minor deflection.
Jelavic had one shot batted away by Guzan but the form guide appeared to be against the Toffees, who had not scored three in a league game since late September.
But Fellaini's header in the third of six added minutes changed that, and the Belgium international could have won it even later but shot straight at the goalkeeper.