كتب : Hatem Maher
Jordan Stewart's own goal in the 33rd minute gave Arsenal the lead before Thierry Henry added the second just before the break.
Togolese striker Emmanuel Adebayor completed the rout seven minutes past the hour mark to hand Wenger a boost in his tenth anniversary with the Gunners.
The victory put Arsenal in fourth place of the Premiership table with 14 points while newly-promoted Watford lie second from bottom on just four points.
As expected, Arsenal dominated the entire match with an attacking trio of Henry, Adebayor and English youngster Theo Walcott, who led the England under 21 team to a place in the European championship after netting a brace against Germany.
The English giants were ahead in the 33rd minute when Cesc Fabregas flicked a free-kick inside the area and Adebayor headed the ball into the path of Kolo Toure but when Stewart tried to clear the ball, he wrongly headed it into his own net.
Henry extended the lead two minutes before the interval when he outpaced Watford defender Jay DeMerit and went face-to-face with the keeper before drilling home.
Adebayor sealed the victory in the 67th minute with an easy tap-in into the empty net after being set-up by French international Henry.
Elsewhere, Liverpool were held to a 1-1 draw by Blackburn Rovers at the Anfield Road.
South Africa striker Benni McCarthy stunned the home crowd with a goal in the 17th minute before Welsh forward Craig Bellamy salvaged a point against his former side midway through the second half.