Arsenal's performance exposed some clear flaws in Arsene Wenger's team just four days before their Champions League second-leg qualifier against FC Twente.
This was their first defeat of the season and a worrying one which ended with captain William Gallas remonstrating withreferee Martin Atkinson and an assistant referee.
But the visitors deserved all they got after a poor display in the opening 45 minutes.
Arsenal had a first half to forget, while Fulham led from the 21st minute, shortly after Robin van Persie missed a sitter when new boy Samir Nasri's mis-kick from Theo Walcott's cross left the Dutchman a gaping goal to aim at from eight yards.
Fulham went straight up the other end, forced a corner and centre-back Hangeland charged in on Jimmy Bullard's low flag kick while Gallas and Kolo Toure stood and stared. He slotted home without any fuss for his first goal for Fulham.
Arsenal struggled to beat West Brom in the Barclays Premier League last week and a single goal decided the result then at the Emirates Stadium.
This time Gallas and Toure seemed like strangers in defence, and although Emmanuel Adebayor's header from Bacary Sagna's cross hit the right post soon after Fulham's opener it was an isolated incident of danger.
Fulham could have had at least two more goals before the break.
Arsenal tried to impose their possession game in the early stages but were caught out when Zoltan Gera slipped a fine ball through to Bobby Zamora in the inside left channel in the eighth minute.
Zamora glided in behind the defenders but carelessly chipped a poor shot over the crossbar from a difficult angle when he should have waited for support to arrive.
Arsenal were then grateful to Gael Clichy for getting back to dispossess Zamora shortly afterwards when the former West Ham striker came raiding again, this time down the Fulham right.
Arsenal's first shot finally came after 12 minutes when Van Persie's pass found Adebayor and the Togo international neatly controlled the ball but fired a low drive off target from 20 yards.
Danny Murphy drove a volley over the bar when Gunners, briefly down to 10 men with Emmanuel Eboue limping off, could only half-clear Gera's cross.
Arsenal had hardly sparkled but should have gone ahead in the 18th minute through van Persie, who was promoted from substitute last week.
And they paid a heavy penalty when Fulham grabbed the lead the opportunist effort by 6ft 5ins Hangeland.
Fulham's luck held when Adebayor's header from a Sagna cross came back off a post but, still without injured £10.5 million signing Andrew Johnson, were good value for their advantage at the interval.
A few sharp words from Arsene Wenger at the interval no doubt brought Arsenal's massive improvement in the second period, but although the pressure on Fulham grew by the minute, there were few chances created.
Van Persie shot wide with a crisp effort trying to make amends for his first-half blunder and new boy Nasri ran his socks off.
But the replacement of a nearly anonymous Theo Walcott by the muscular Nicklas Bendtner made little difference and there was just no penetration to go with Arsenal's possession.