Arsenal were unsettled by Fulham's physical approach, and it was clear how much they missed the composure and class of the injured Cesc Fabregas in midfield.
But for Fulham, it was the perfect response to their disappointing opening day defeat at newly promoted Hull City.
Arsenal were able to recall Kolo Toure and Robin van Persie - but Fulham's record signing Andrew Johnson was still sidelined by a thigh injury.
Fulham wanted it more - Wenger
It did not stop Roy Hodgson's side showing a greater sense of urgency and a highly charged approach in the first 45 minutes.
John Pantsil was fortunate to escape a red card in the 13th minute for a nasty challenge on Arsenal's Emmanuel Eboue.
Arsenal almost broke the deadlock six minutes later when Van Persie fired Samir Nasri's pass just wide - but it was Fulham who took the lead two minutes later.
Fulham worked a short corner and Bullard whipped in a cross that allowed Hangeland to steal in ahead of William Gallas to poke home from close range.
Arsenal responded and Adebayor almost levelled instantly when he directed a superb header against the post from Sagna's cross.
Fulham new boy Zamora has proved a tormentor of Arsenal in the past, and he was almost at it again on the hour when he turned a driven centre from Seol Ki-Hyeon inches over the top with Manuel Almunia beaten.
Hodgson delighted with Fulham show
Arsenal needed greater attacking thrust, and it was no surprise when Arsene Wenger made a change with 25 minutes remaining, sending on Nicklas Bendtner for the subdued Theo Walcott.
It made little difference, with Arsenal enjoying plenty of possession but failing to carve out any clear-cut chances.
Adebayor had a shot from outside the box with six minutes left, but it was saved with the minimum of fuss by Fulham keeper Mark Schwarzer.
It was a rare moment of danger for Fulham and they survived in relative comfort.
Fulham manager Roy Hodgson: "I was a really good result and it was a good performance, in particular, for just over 70 minutes.
"I thought our passing and movement was good in that time and I was happy with our defending.
"We fell into the trap in the last 15 minutes or so of trying to hang on to the result and there were a few panicky moments. But the defence stood firm."
Arsenal boss Arsene Wenger: "When you want to play at the top you must start the game with the right attitude and personality.
"That's what we didn't do and that's a good learning lesson. It was the kind of game where you couldn't afford a mistake at the back or at a set piece.
"I believe they wanted it a bit more than us in the first half and the corner (when they scored) shows that."
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