كتب : Hatem Maher
Emmanuel Adebayor and Cesc Fabregas were also on the score sheet to help Arsenal in their bid to snatch a UEFA Champions League spot.
The win put Arsenal in fifth place with 44 points, two points adrift of fourth-place Tottenham Hotspur who play Blackburn Rovers on Sunday.
Henry broke the deadlock in the 31st minute after he sidestepped Moritz Volz inside the area before firing a close-range shot into the roof of the net.
Adebayor doubled the lead four minutes later when he received Fredrik Ljungberg's through pass and drilled a low shot past Fulham keeper Tony Warner.
Henry killed off Fulham's hopes of returning to the game when he went face to face with Warner before sending a cool finish into the far corner of the net.
Spanish youngster Fabregas completed the route in the 86th minute when he met Mathieu Flamini's back pass with a fine strike into the net.
In other matches, Aston Villa beat Portsmouth 1-0, Middlesbrough defeated Birmingham 1-0, Newcastle cruised past Bolton Wanderers 3-1 and West Ham tied Everton 2-2.