The Hornets, who were winless in seven league games, made an incredible start to race into a 2-0 lead inside 13 minutes on Tuesday, with two former Tottenham players central to Arsenal's downfall.
Younes Kaboul's deflected free-kick opened the scoring, while Etienne Capoue pounced on Gabriel's loose throw before venturing forward unchallenged and drawing a save from Petr Cech, from which Troy Deeney pounced on the rebound.
It should have served as a wake-up call to Arsenal, for whom manager Arsene Wenger is still serving a touchline ban, but it was the visitors who remained on the front foot and they saw efforts from Sebastian Prodl and Miguel Britos repelled before the end of a first half in which Aaron Ramsey was forced off injured.
Theo Walcott, fresh from his hat-trick in Saturday's 5-0 FA Cup win over Southampton, came on for the second half and Arsenal immediately carried a greater threat, the England forward finally calling Heurelho Gomes into meaningful action.
It was Alex Iwobi who pulled one back, volleying in Alexis Sanchez's cross as Wenger's men made their dominance of the ball count.
Substitute Lucas Perez struck the crossbar five minutes from time but, having weathered the storm, Walter Mazzarri's side clung on to claim a win that ought to quieten speculation over the Italian's future.
Watford, who handed a debut to AC Milan loanee M'Baye Niang, broke the deadlock in fortuitous circumstances after 10 minutes. Kaboul's speculative 25-yard strike was powerful but would not have unduly troubled Cech had it not been for a sizeable deflection off Ramsey.
The Welshman's evening got worse when Gabriel's throw-in eluded him and Capoue seized on the loose ball, his run ending with a shot that came off Cech's leg and left Deeney with a tap-in.
Ramsey's miserable cameo came to an end midway through the half, the midfielder limping off with an apparent calf injury.
Watford, who confirmed the big-money sale of Odion Ighalo to Chinese Super League club Changchun Yatai prior to the match, continued to press and Prodl's header forced a fingertip stop from Cech, while Britos' effort was blocked by Olivier Giroud.
For their part, Arsenal looked a world away from the side that was so dominant at St Mary's Stadium, with the home fans growing increasingly restless.
Walcott's introduction in place of Giroud helped to get the Gunners going and he fired an angled shot narrowly wide within three minutes of the restart.
The former Saints forward was presented with a glorious chance to reduce the deficit two minutes later, shooting tamely at another of Watford's ex-Spurs charges as Gomes saved with his legs before brilliantly thwarting Iwobi.
But Iwobi was not to be denied when, in the 58th minute, he connected with Sanchez's chipped delivery to find the far post and breathe new life into Arsenal's challenge.
Mazzarri's side, beaten by League One Milwall in the FA Cup on Sunday, suddenly looked vulnerable every time Arsenal attacked and had to dig deep to stifle a forward line now led by Sanchez through the middle.
It was an unlikely source from which the next moment of danger came, Nacho Monreal firing in a fine volley that swerved wide of Gomes' right-hand upright.
With time running out, the Gunners saw Perez rattle the woodwork with a strike that had Gomes beaten, but the Hornets were perhaps deserving of that late piece of luck as they inflicted Arsenal's first home league defeat since their opening game of the campaign.
Wenger must now lift his side ahead of a visit to league leaders Chelsea on Saturday.