Gunners squander two-goal lead for second time in a week as Jol's side, inspired by Bulgarian target man, saved the heartbreak of defeat by Schwarzer's last-minute spot kick save
Olivier Giroud and Dimitar Berbatov both scored braces for Arsenal and Fulham respectively. Lukas Podolski added a goal for the Gunners while Alexander Kacaniklic rounded out the Cottagers' scoring.
Another unconvincing defensive display from Arsenal is likely to see increased pressure on Arsene Wenger, with the Gunners having won only one of their last six games in all competitions.
The hosts had to make do without the services of Jack Wilshere, who was suspended following last week's red card at Old Trafford and Theo Walcott was included for his first Premier League start since the opening game of the season.
It was the unsettled winger who proved the spark behind the Gunners taking an 11th minute lead; with Walcott winning, then taking the corner that Giroud powerfully headed beyond Schwarzer at the near post.
As Kieran Richardson hobbled off clutching his hamstring, Fulham's cumbersome start was further punished as Podolski doubled Arsenal's lead. Mikel Arteta fortuitously found his way to the byline and his cut back was slammed home by the German, who came through the back-post presence of Sascha Riether all too easily.
That lead was short lived though, with the Gunners made to suffer for giving Berbatov an abundance of space in the six-yard area as he nodded home Bryan Ruiz's inviting corner.
Berbatov - who had been the inspiration for the visitors- then turned provider five minutes before the interval. The Bulgarian was released down the right hand flank after some smart Cottagers build up and his first time cross was met by Kacaniklic - Richardson's replacement - who stooped to head an angled effort past Vito Mannone.
Jol's side almost completed a remarkable turnaround on the stroke of half time, though with Ashkan Dejagah unable to connect properly with John-Arne Riise's cross, Gunners center back Per Mertesacker denied the onrushing Berbatov at the far post.
Walcott looked the most likely to help the Gunners reestablish their lead after the break, first sending in a cross that narrowly evaded Giroud with the goal gaping, before drifting in from the right flank to send a curling left-footed effort just wide of the upright.
However, it was Fulham who made the breakthrough courtesy of a cooly-struck Berbatov penalty after Arteta hauled down Ruiz after the Costa Rican had just dispoossed him in his own penalty area.
The Cottagers could, and should, have extended their lead but Kacaniklic could only fire straight at Mannone before Giroud drew the home side level. The Frenchman hit the post after some bizarre defending from Brede Hangeland though made no mistake after Walcott clipped the ball back into the area, heading home with power similar to his first.
As the game entered its final stages both teams attempted, unsuccessfully, to snatch all three points. A last-gasp Laurent Koscielny tackle denied Berbatov at the far post, while Giroud saw his driven left-footed effort turned round the post by Schwarzer.
Substitute Andrey Arshavin earned the Gunners a disputable penalty as his cross hit Chris Baird on the arm in the game's closing seconds though Schwarzer was equal to Arteta's effort from 18 yards, with the game ending a 3-3 draw.
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