Watford defended well, and were at times were able to put pressure on the home side, though these attempts were ultimately fruitless thanks to some good saves by Petr Cech, searching for his 200th Premier League clean sheet.
Pierre Emerick Aubameyang and Henrikh Mkhitaryan each contributed a goal and an assist after Shkodran Mustafi's header had given the Gunners an early lead in a clinical attacking display at the Emirates Stadium.
The scoreline was flattering for Arsenal, which ended a three-game Premier League losing streak, but Watford only had itself to blame after spurning multiple chances, most notably captain Troy Deeney's tame penalty.
The Watford striker has become a villain in the eyes of Arsenal fans after saying that they ' lack cojones' following their last meeting at Vicarage Road. For moments we played very well and for moments we had to stick together and suffer.
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Mustafi headed home from a Mesut Ozil free-kick for Arsenal's 1000th home goal in the Premier League.
"But the most important thing is when the team wins".
Arsenal are also vying for a spot in next season's Champions League through the Europa League.
With the score at 2-0, Deeney saw his penalty kick saved by Petr Cech, and while Gunners fans absolutely loved it, they are also giving props to the striker for what he did after his side's defeat.
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"He had to wait a while to save a penalty, and it's quite fortunate that it's against Deeney", added Wenger.
"Of course I worry because I want our fans to be behind the team, but after what happened in that week it is understandable".
Arsenal manager Arsene Wenger, speaking to BBC Sport: "It was a hard game like you get in the Premier League. We had a nightmare week, and so overall we still have some work to do, but we are in a good way".
I doubt you've forgotten that Stan Kroenke is a business man and Arsenal is a business for him. They all say no, but we know all - it's not true. We have shown spirit and we are in a strong position now against Milan.
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Ozil's assist was his eighth of the season in the Premier League and came just a few days after he set up both goals in Arsenal's 2-0 win over AC Milan in the first leg of their Europa League last-16 tie at the San Siro.