Unai Emery's side were second best to the Hornets for much of the second half and were indebted to Premier League debutant Bernd Leno – who replaced the injured Petr Cech on the stroke of half-time – for two fine stops.
That gave them the platform to win the game late on as Craig Cathcart's own goal in the 81st minute put them ahead and then Mesut Ozil's strike two minutes later secured all three points.
After an impressive start to the season – which saw them win their opening four games – Watford have now gone three without a win and are in danger of slipping down the Premier League table.
After a lively opening Alexandre Lacazette squandered a golden opportunity in the 15th minute, clipping a tame effort over the onrushing Ben Foster and wide of the post after latching onto Abdoulaye Doucoure's poor headed pass.
Leno wasted little time in making his mark after replacing Cech - who pulled up holding his hamstring after a goal kick - getting down smartly to push Troy Deeney's flicked effort from Roberto Pereyra's free-kick around the past six minutes into the second period.
Lacazette's woes in front of goal continued soon after, skewing his header horribly wide after a sweeping counter attack, before Leno again came to his side's rescue, racing off his line to block Andre Gray's effort.
Substitute Isaac Success clipped agonisingly wide late on before Cathcart turned Alex Iwobi's cross into his own net under pressure from Lacazette.
Ozil then sealed the win with a cool finish from Lacazette's cross in the 83rd minute as Emery's men marched on.
What it means: Gunners keep on firing
With wins in the Europa League and the EFL Cup as well that is seven triumphs on the spin for Emery's side now. Those opening defeats to Manchester City and Chelsea are a distant memory as the Gunners continue to climb the table. Watford, meanwhile, need to arrest the slide, with their own fine start to the season in danger of unravelling.
Leno makes impressive bow
The German has had to bide his time for a Premier League appearance, but he did not disappoint when it came. His full-stretch save from Deeney showed fantastic athleticism, while his stop from Gray was all about being alert and quick off his line.
Lacazette firing blanks
The Frenchman has enjoyed an impressive start to the season, but he will not look back on this game too fondly. His two spurned chances could have had the Gunners out of sight long before Cathcart's unfortunate intervention with nine minutes remaining.
Key Opta stats:
- Arsenal have won five consecutive Premier League games for the first time since August 2017 (a run of six).
- Arsenal have registered back-to-back clean sheets in the Premier League for the first time since April last season.
- Since returning to the top-flight in 2015/16, Watford have scored seven own-goals, more than any current Premier League side.
- Arsenal have scored 10 Premier League goals in the second-half this season, a joint-high tally along with Manchester City.
- Arsenal playmaker Mesut Ozil has scored two goals in his last three Premier League games, as many as he managed in his previous 18.
Arsenal travel to Azerbaijan on Thursday for a Europa League clash against Qarabag before returning to domestic action with a short trip to Fulham on Sunday. The Hornets, meanwhile, welcome Bournemouth to Vicarage Road next Saturday.