With Thursday's second leg of Fulham's semi-final against Hamburg in mind, boss Roy Hodgson made nine changes for this game, coming within seconds of ending a run of 16 successive defeats at Goodison Park.
Although Erik Nevland gave Fulham a 36th-minute lead against the run of play, Victor Anichebe hauled Everton level five minutes after his arrival as a half-time substitute before Arteta stroked home a face-saving winner deep into injury time.
You can hardly blame Hodgson for making as many changes as he did, with arguably the most high-profile game in the club's history looming.
Hodgson rested eight players - Paul Konchesky, Aaron Hughes, Danny Murphy, Dickson Etuhu, Damien Duff, Zoltan Gera, Brede Hangeland and Simon Davies - with Bobby Zamora nursing an Achilles injury.
For the first 36 minutes of the game they were over-run and barely in the match as Everton created, and wasted, a host of chances.
The first of those came after 30 seconds as Mark Schwarzer, one of only two survivors from Thursday's goalless first leg in Hamburg, smothered a 20-yard snap shot from Tim Cahill, making his 200th appearance for the Toffees in all competitions.
That set the tone, yet remarkably Schwarzer was never called upon again until late in the first half when he stopped on the line a deflected effort from Yakubu.
However, the right-hand post came to his aid in the second minute as Diniyar Bilyaletdinov cracked a left-foot volley against the base after Tony Hibbert had floated over a right-wing cross.
One-way traffic followed with Cahill off target with a free header, Yakubu dragging a shot past the post after an error from defender Chris Smalling, whilst Cahill also drilled another low effort wide.
What would have been an untried Fulham rearguard defended stoutly, putting bodies in the way.
But then nine minutes from the break Fulham scored their first away league goal since a 3-2 defeat at Stoke on January 5, ending a blank seven-game run.
It came courtesy of a howler from Leighton Baines, who played a nonchalant pass to Tim Howard without looking, allowing Nevland to nip in and flick the ball over the advancing American goalkeeper.
Nevland's fourth this season also ended Fulham's goal drought on Merseyside - against both Everton and Liverpool - at nine hours and 14 minutes, with their last in a 4-1 defeat at Goodison in April 2007.
Fulham should have added a second shortly before the break when Stefano Okaka lofted a delightful chip into the area for Clint Dempsey to run onto, but with only Howard to beat, he volleyed over the crossbar.
At half-time boss David Moyes brought on Anichebe for Bilyaletdinov, which proved inspired as the striker levelled five minutes later.
Arteta, nursing a stitched cut over his left eye following an incident at the end of the first period, supplied a dinked cross from the left-hand edge of Fulham's penalty area.
Yakubu attempted a dramatic scissor kick, fortunately just avoiding Anichebe's head as he bravely nodded into the ground from six yards for what proved to be his second goal of the season as it took a slight deflection beyond Schwarzer's outstretched grasp.
Fortune then favoured Fulham as referee Lee Mason failed to spot an Anichebe cross hit Nicky Shorey's left arm in the area on the hour.
Ten minutes later Jonathan Greening's intercept to Tony Hibbert's right-wing cross flashed a yard beyond Schwarzer's right-hand post.
Then within a minute a goal-bound downward header from Louis Saha, on as a 61st-minute substitute for captain Phil Neville, bounced off Dempsey and inches over the bar.
It meant Fulham were still in the game, and they should have stolen victory, only for Stefano Okaka to shoot tamely into the welcoming arms of Howard after being played in by Nevland on a 76th-minute break.
It was then Everton who had the chance to win it, but a defiant Schwarzer brilliantly saved from Cahill at point-blank range in the 80th minute, prior to a more routine stop from Arteta four minutes from time.
But with a draw on the cards, a Chris Baird foul on Cahill inside the area allowed Arteta to score from the spot with virtually the last kick of the game.