Everton were stunned after Steve Sidwell fired a late equaliser that allowed Fulham to escape with a point from their Premier League clash at Craven Cottage.
Apart from their seventh-minute opener by Bryan Ruiz and Sidwell's 90th-minute strike, Martin Jol's side were over-run by the rampaging visitors.
Only desperate defending and wayward finishing, chiefly from Nikica Jelavic, prevented Everton from adding the scores their superiority deserved - until Marouane Fellaini intervened.
The roaming Belgium forward took his tally for the season to five goals in 10 matches with two clinical finishes, demonstrating his strength to hit the second.
Fulham manager Martin Jol identified Everton in the build up to the game as the ``best of the rest'', the benchmark to which a club like his must aspire, and he will be cherishing the luckiest of points.
Leading 2-1 and creating chance after chance against a team rarely overwhelmed at home, they failed to produce the third goal they needed to kill the game off and paid a high price.
David Moyes could barely believe his eyes when substitute Sidwell stabbed home Sascha Riether's cross as injury time beckoned and the furious Everton manager stalked from the pitch at the final whistle.
A mazy early run from Kevin Mirallas, who had recovered from an ankle injury to start, was bettered by Dimitar Berbatov moments later.
The Bulgarian weaved a path across the edge of the penalty area and the only way Everton could halt his progress was for Phil Neville to hack him down.
It proved a costly mistake as at the ensuing free-kick Bryan Ruiz curled the set piece over the wall towards the right side of the net.
Keeper Tim Howard got a hand to the ball but only pushed it on to the woodwork and the rebound struck him on the back and crossed the line.
Fulham held the lead but it was Everton who were spending more time on the ball, launching a series of attacks lacking only in a killer final ball.
The lively Steven Pienaar, back from suspension, lofted two dangerous long passes into the box, giving the Cottagers defence little margin for error.
Slick interchange between Ruiz, Riether and Damien Duff created space on the right but Phil Jagielka intercepted the final pass with Berbatov lurking.
Much of Everton's passing was quick and inventive with Nikica Jelavic wasting a half-chance created by a pinpoint cross from Leighton Baines.
A curling shot from Seamus Coleman was saved by Mark Schwarzer and only stout defending from Fulham was preventing Everton from equalising.
Jagielka blasted just wide of the left post from long range and then Jelavic's attempt to chip Schwarzer sailed over the crossbar.
The second half started in a similar vein with Fulham's goal being peppered by the visitors.
Brede Hangeland produced a commanding header to clear and seconds later Jelavic nodded a cross from Baines to the far post, where Marouane Fellaini just failed to connect.
The equaliser was inevitable given Everton's dominance and it arrived in the 55th minute through Fellaini.
Mirallas switched on the afterburners to dash free down the right before finding out Fellaini, who drilled the ball home from eight yards out.
With time to compose himself and pick his spot, Berbatov was kept out by Howard from a tight angle as Fulham sought to deliver a swift response.
Jelavic, played in by Fellaini, was about to pull the trigger from six yards out but Riether executed a perfect tackle.
Chances continued to come thick and fast and finally Everton's second arrived with Fellaini chesting down Coleman's long ball, holding off two defenders and stabbing home.
Hangeland nodded over the crossbar, while at the other end the irresistible Fellaini struck the right post and was denied by a fine save from Schwarzer.
Disaster struck for Everton in the dying moments when Berbatov missed Riether's cross, but Sidwell was there to fire the equaliser.