Alexis Sanchez opened the scoring on 62 minutes – his 10th goal in his last six games for club and country – after good work from Mesut Ozil and Santi Cazorla in a rapid Arsenal counter-attack.
Germany international Ozil turned provider again four minutes later, cutting back for Olivier Giroud to double the Gunners’ advantage.
Aaron Ramsey made it three on 74 minutes, guiding home via a deflection after a break from Hector Bellerin. The right-back surged into the box and set up Ramsey, who capped a brilliant week for Wales and Arsenal with his first goal of the Premier League season.
The win sees the Gunners rise to second place, two points behind league leaders Manchester City, while Watford sit 14th with 10 points from their opening nine Premier League games.
Ramsey squandered Arsenal’s best chance of the first-half on 27 minutes, scooping over from four yards after a pinpoint cross from Sanchez.
It marked the start of a frantic few minutes, as moments later Odion Ighalo panicked in front of goal after he was set clear.
The Watford striker, who has scored five of Watford’s six Premier League goals this season, was bearing down on Petr Cech but side-footed wide from eight yards under pressure from Nacho Monreal.
Sanchez was bright throughout, testing Heurelho Gomes with a stinging 25-yard strike inside the first five minutes, but Etienne Capoue and Ben Watson were coping with Ozil’s threat well in an even first 45 minutes.
Both sides had opportunities as the half wore on, as first Troy Deeney broke clear only to let down Ighalo with a poor final ball, before Bellerin burst past Nathan Ake after linking-up with Ramsey, but the right-back failed to pick out an unmarked Monreal at the back post.
Arsenal caught Watford on the counter several times in the second half, and the Hornets fell behind just after the hour mark. Capoue went down on the edge of the Gunners box with Watford committed forward, but the referee was unmoved and Arsenal broke through Cazorla and Ozil.
The Germany midfielder skipped through and was upended in the Watford box by Ake, but Sanchez followed up to sweep past Gomes.
The Hornets struggled to react to the opening goal and tired in the second half, with Capoue and Deeney suffering cramp, and substitute Giroud capitalised on more poor defending to put Arsenal two-up on 68 minutes.
Sanchez and Ozil again were involved, as the latter teed up Giroud to help the ball past Gomes with his right foot.
Ramsey then punished Watford to strike Arsenal’s third as his deflected effort wrong-footed the Watford ‘keeper. Bellerin provided the assist after a surging run down the right-hand side, capping an excellent game from the young full-back.
Deeney continued to work selflessly for his side even into the final stages, but the Watford striker has now had the most shots without scoring in the Premier League this season (23).
Watford: Gomes (6), Nyom (5), Prödl (6), Cathcart (6), Ake (5), Capoue (6), Watson (6), Abdi (5), Deeney (6), Anya (6), Ighalo (6)
Subs used: Paredes (6), Ibarbo (6), Berghuis (6)
Arsenal: Cech (6), Bellerin (7), Mertesacker (6), Koscielny (6), Monreal (6), Coquelin (6), Cazorla (6), Ozil (7), Alexis (7), Ramsey (7), Walcott (6)
Subs used: Arteta (6), Oxlade-Chamberlain (6), Giroud (7)
Man of the match: Alexis Sanchez