The Merseyside club ended the home side’s nine-game unbeaten run at Craven Cottage this season, scoring two late goals after a Bryan Ruiz strike looked to have leveled it.
Everton won for the first time at Craven Cottage with a 3-1 victory over Fulham in a lively encounter on Sunday.
Fulham will feel aggrieved to have come away from the game with nothing after two late strikes from Jack Rodwell and Louis Saha cancelled out an impressive debut goal from Bryan Ruiz.
It was Everton which began the game in a more fluent fashion and it was rewarded with a goal just two minutes into the match.
Fulham captain Danny Murphy was careless on the ball, Jack Rodwell capitalized and did a neat one-two with Greek striker Vellios before laying off Drenthe, on loan from Real Madrid, who smashed his strike left-footed into the bottom right-hand corner.
Everton’s pressure did not subside either and it continued to see the lion’s share of the ball, its next chance for a second goal coming on 11 minutes when a Leighton Baines cross from the right wing was headed over by omnipresent midfielder Rodwell.
Fulham started to spark to life soon after, but its chances were limited to long-range strikes from Steve Sidwell and former Liverpool left back John Arne Riise.
Drenthe was a threat all half, the Dutch winger’s peppering of the goal, testing goalkeeper Mark Schwarzer.
At the other end, Tim Howard made a brilliant save to prevent Clint Dempsey drawing the Cottagers level 25 minutes in.
The ex-Manchester United keeper was the hero for the away side not long after too, when towering Fulham center back Brede Hangeland’s header was dipping in until the American got his fingertips on the ball and tipped it over the bar.
Fulham continued to press and ended the half on top, Dempsey bending an 18-yard shot just wide of the right-hand post.
After the break the home side continued to hog possession, skipper Murphy and former Toffees forward Andy Johnson whipping in a number of crosses that suited their obvious aerial threat.
It took 10 minutes for Everton to shift out of second gear but soon enough the club was fighting for the ascendency. Striker Louis Saha, who replaced the largely ineffective and isolated Apostolos Vellios early in the second half, was caught marginally offside after breaking clean through the backline.
But it was Martin Jol’s first substitution of the match that immediately altered the shape of the game – Ruiz came on for Murphy to score his first goal for the club he joined on transfer deadline day from FC Twente.
The 10.6 million pounds summer signing lobbed exquisitely from the left-hand side of the box over the defense and Howard to draw the home side level with 32 minutes remaining.
However, the goal seemed to stifle the Fulham attack and it rallied the away side. Leighton Baines fired a free kick over the bar, and Tim Cahill – who came off the bench to win the game in place of Neville – appeared to have been grappled to the floor in the box but no penalty was given.
Striker Louis Saha, who replaced the largely ineffective and isolated Apostolos Vellios early in the second half, forced Schwarzer to make a good save to prevent the team going behind again.
At the other end Fulham was hoping referee Lee Probert would point to the spot when defender Zdenek Grygera.
Everton was forced to defend frantically in the last few minutes before stoppage time, Phil Jagielka blocking Johnson’s shot before Bobby Zamora’s cross back into the box is hit by Ruiz at the Toffees keeper, and eventually cleared by Baines.
Seconds after Zamora inexplicably blasts over when gifted an open goal, substitute Saha gave David Moyes the much-needed victory against the run of play, dinking his shot into the bottom corner when one-on-one with the Fulham shot-stopper.
To cap the unlikely late win off, Rodwell scored Everton’s third in stoppage time to give the away side only the second win at Craven Cottage in 11 attempts, his shot hitting the ground and bouncing beyond Schwarzer to propel the Toffees away from the looming relegation zone while leaving Fulham in the thick of it.