Thousands of seats remained empty at the Emirates, as fans boycotted the home match, after disappointing recent performances.
And goals from Shkodran Mustafi, Pierre-Emerick Aubameyang and Henrikh Mkhitaryan saw Wenger to number 700, while Troy Deeney - who accused Arsenal of lacking "cojones" earlier in the season - had a penalty saved by Petr Cech.
"We are in a job where we have to get the fans on our side and do absolutely everything to achieve it".
Mustafi headed home from a Mesut Ozil free-kick for Arsenal's 1000th home goal in the Premier League.
Arsenal are 2-0 up in their last 16 Europa League tie against AC Milan and will hope to go the distance in the tournament, which could well be their best way to qualify for the Champions League next season.
As he will play no part in the second leg of a Europa League last-16 encounter with AC Milan on Thursday, and with Arsenal out of the FA Cup and the next worldwide break approaching, Aubameyang will have to wait until April 1 for his next outing against Stoke.
Aaron Ramsey and Laurent Koscielny were rested, with Jack Wilshere only on the bench, but the gamble paid off for Arsenal. "Just thanks to the fans who were supporting".
Fuelled by that jibe, Arsenal took the lead in the eighth minute.
Watford controlled the game either side of halftime, but was punished for failing to make its dominance pay when Aubameyang doubled the lead in the 59th as he rounded Karnezis after latching onto Mkhitaryan's through ball.
Arsenal picked up the pace again and returning Mkhitaryan's earlier assist, Aubameyang supplied the cross to give the Armenia worldwide his first league goal for Arsenal.
"Thanks to the result in Milan, we are in a good position to reach the last eight of the Europa League".
Defeat keeps Watford 10th and nine points clear of the relegation zone.
Watford should have been level shortly before the half-hour when Cech pushed away a Richarlison free kick and Roberto Pereyra, following up, thrashed an effort wildly over when he had time to take a touch and then shoot.
After that match, he said: "There's a reason they lost".
'Let's say that someday it might interest me.
'I remember very well every time he refused the biggest clubs to stay at Arsenal.