The Gunners looked jaded and vulnerable but were never really exposed by a very poor Fulham side which lacked inspiration and leadership.
However, the visitors did have the first real chance of the game in the eighth minute when Gael Clichy headed Papa Bouba Diop's header from a left-sided corner off the line.
Arsenal's first chance came in the 12th minute when Robert Pires broke free just inside the Fulham half. He appeared to over-hit his pass but retrieved it just as quickly and then cut inside the left side of the Fulham area only to fire his shot straight at Edwin Van der Sar.
Arsenal's next attempt led to a goal. The referee waved play on when Pires appeared to be hauled down in the middle of the park.
However, as the French midfielder was falling to the ground he managed to stab the ball to Thierry Henry who accelerated towards the left flank.
He then cut back onto his right side in a move that put Ian Pearce on his backside before firing a shot into the right-hand corner of the net with Van der Sar only able to help it on its way.
The Gunners continued to control the game and Patrick Viera, Pires and Fredrik Ljungberg all had good opportunities to score. Fulham were woeful and even though Arsenal appeared to be playing in a trance, the visitors could not take advantage.
The game continued in the same vein after the interval although Henry momentarily worried the Fulham keeper when he flashed a free-kick across the Dutchman's goal.
Henry could have scored his second after 53 minutes if 17-year-old Cesc Fabregas had spotted him speeding down the right flank. However, the young Spaniard picked out Pires instead and he was quickly closed down.
Kolo Toure should have scored when he met a corner at the back post but directed his header high over Van der Sar's goal.
The Dutch goalkeeper saved again from Pires just before the hour when the French midfielder worked his way to the left side of the area and fired a shot in from an acute angle.
Arsenal keeper Manuel Almunia was on hand to deny Tomasz Radzinski in the 65th minute when he came out quickly to collect an attempted lob.
Arsenal thought they had scored four minutes later when Henry hit a thunderous half-volley that beat Van der Sar but hit the angle of the crossbar and cannoned away to safety.
The Gunners doubled their lead two minutes later however when Pires took advantage of some fine approach playing by Fabregas. He opened up the Fulham defence with a delightful pass which Dennis Bergkamp stepped over.
Pires collected the ball in space, moved to the left side of the area and fired his shot into the net beyond the oncoming Fulham goalkeeper.
The remainder of the game saw Arsenal simply playing training ground football as they wound down the clock to collect all three points.