Fulham 0 Arsenal 3
Those two goals put paid to Roy Hodgson's plans of eking out a draw, he utilised a 4-5-1 formation, and Tomas Rosicky completed the scoring in the second half, sliding after Eduardo's impressive run and centre.
Before kick-off all 6ft 5ins of Norway international centre-back Brede Hangeland was unveiled to great cheers from the home supporters. But the former FC Copenhagen giant could only watch from the stands as after only 19 minutes the Togo international rose above Dejan Stefanovic to nod home from Arsenal's first meaningful chance.
Rosicky, back in the Gunners' side after recovering from a viral infection, played a reverse ball to overlapping full-back Gael Clichy on the left-hand touchline. The pacy Frenchman, with bags of time, hit a first-time cross which found the head of Adebayor, whose neat header left Antti Niemi with no chance of saving.
Lightning struck twice for Fulham as six minutes before the interval the Togo forward used his head to good effect again, though this time around his supply was from the right-hand side. Alex Hleb's driven ball pin-pointed Adebayor, who again jumped higher than his opponents. Captain Aaron Hughes was the guilty party for goal number two.
Fulham failed to muster a single shot on target as Hodgson's tactics looked feckless and limp. American Clint Dempsey huffed and puffed on his own up front for his team; but he was never going to blow the Cottage down.
The biggest cheers of the afternoon occurred when Jimmy Bullard entered the fray at half-time, but despite his creative touch, the result was in the bag for the visitors by the time he was introduced.
Never, in any of the 26 league games that Adebayor has scored in, have Arsenal lost a match. With the striker in such white-hot form, manager Arsene Wenger must be delighted that Togo failed to qualify for the African Nations Cup which begins in Ghana on Sunday.
Rosicky scored his side's third and final goal in a flaccid second half, sliding in after a superb dribble and pull-back by Brazilian-born Croat Eduardo, who impressed again.
Arsenal remain on the coat-tails of Manchester United, equal on points but behind on goal difference, after late goals from Wayne Rooney and Cristiano Ronaldo secured a win at Reading.
Fulham remain in 19th place in the Premier League and Hodgson must hope he can bring more players to the club and soon.