The Gunners, who had beaten Manchester United before the international break, were made to work hard for their victory following a spirited effort by the well-organised Hornets.
Ultimately, though, the technical superiority of Arsene Wenger's men proved enough, as in-form Alexis Sanchez netted after a breakaway on 62 minutes, with goals from substitute Olivier Giroud and Aaron Ramsey helping to keep Arsenal only two points behind leaders Manchester City.
Theo Walcott was again deployed as a central striker, supported by the all-action Sanchez and playmaker Mesut Ozil.
Arsenal put the pressure on from kick off, with Sanchez's rising 25-yard effort forcing Watford keeper Heurelho Gomes into a smart save on nine minutes.
At the other end, Petr Cech had to be alert to beat away a fierce drive from Troy Deenay after the forward had won the ball just outside the penalty area.
Despite holding a high line, Watford also offered plenty of attacking threat with the physicality of Deenay a problem for the Arsenal defence.
The Hornets, though, were cut open on 28 minutes.
Clever footwork from Ozil played Sanchez into space, and his lofted, angled pass fell at the far post to Ramsey, but at point-blank range, the Wales midfielder sent a sidefoot effort up off the top of the crossbar.
Watford then broke quickly as Odion Ighalo raced clear into the right side of the Arsenal penalty area, but tumbled under pressure from Nacho Monreal, stabbing the ball wide before appealing in vane for a penalty.
Just before half-time, Cech raced off his line to clear a long pass from Etienne Capoue which the Watford players claimed was with his arm rather than shoulder, but referee Mike Jones waved away the appeals.
Watford upped the tempo following the restart, out-fighting Arsenal in all areas.
Capoue led the charge and was screaming for a penalty after going down under a challenge from Francis Coquelin.
The referee, however, waved played on, and Arsenal immediately broke to take the lead on 62 minutes.
Sanchez dashed down the left and fed Santi Cazorla at the edge of the Watford box
His slide-rule pass picked out Ozil, who was brought down by a diving challenge from Craig Cathcart
Before the referee could point to the penalty spot, Chile forward Sanchez had lashed the loose ball in off the far post for his 10th goal in six appearances for club and country.
Before Watford could mount a recovery, Arsenal had doubled their lead.
Ozil was again involved, cutting a deflected pass back through the six-yard box where Giroud, who had only just replaced Walcott, swept the ball into the roof of the net on 68 minutes.
Ramsey - on target for Wales in their midweek Euro 2016 qualifier against Andorra - finally got back on the Arsenal goal trail when he tapped home a deflected effort, off defender Ikechi Anya, following a darting run down the right by Hector Bellerin in the 73rd minute.
TWEET OF THE MATCH
"Game of 2 halves: one awful, one terrific
But overall, an excellent away win
#afc"
- Piers Morgan @piersmorgan
https://twitter.com/piersmorgan/status/655448380819148800
PLAYER RATINGS
Watford
Heurelho Gomes: 6
Allan Nyom: 6
Sebastien Prodl: 6
Craig Cathcart: 6
Nathan Ake: 6
Odion Ighalo: 6
Ben Watson: 6
Ikechi Anya: 6
Troy Deeney: 8
Almen Abdi: 6
Etienne Capoue: 7
Subs
Steven Berghuis: 6
Victor Ibarbo: 6
Juan Paredes: 6
Arsenal
Petr Cech: 7
Hector Bellerin: 7
Per Mertesacker: 6
Laurent Koscielny: 6
Nacho Monreal: 7
Santi Cazorla: 7
Francis Coquelin: 7
Aaron Ramsey: 7
Mesut Ozil: 8
Alexis Sanchez: 7
Theo Walcott: 6
Subs
Olivier Giroud: 7
Alex Oxlade-Chamberlain: 6
Mikel Arteta: 6
STAR PLAYER
Ozil is so often maligned, but the German playmaker was at the heart of all things positive for Arsenal at Vicarage Road
His understanding with Sanchez is bordering on telepathic, and it was Ozil's deft touches which helped set up the opening goals
Arsenal's record signing will, of course, still find plenty of critics due to his somewhat lackadaisical style - but they should watch a rerun of this match in slow motion to truly appreciate Ozil's contribution.
MOMENT OF THE MATCH
Few teams turn defence to attack as well as the Gunners
Their opening goal on 62 minutes was a case in point
No sooner had Watford's attack broken down with a penalty appeal turned away, then Sanchez was scampering down the left
Roll the clock on about 60 seconds and the Chile forward was wheeling away in celebration
Clinical.
VIEW FROM THE BENCH
Quique Sanchez Flores set his side up with two banks of four and after looking to be holding a high line, the hosts soon proved difficult to break down
Arsenal tried too many quick passes in the first half when a more direct approach was needed to release Walcott
Eventually, though, Arsenal's patience paid off as a quick break saw Sanchez give them the lead, with Giroud and Ramsey making sure of another impressive away win for Arsene Wenger's side.
MOAN OF THE MATCH
Arsenal's technical superiority again proved enough to earn them victory, but questions remain about character as at the start of the second half, the Gunners were outfought by the Hornets
While it did not ultimately matter here, it could just yet prove their Achilles heel over the course of the championship race.
WHO'S UP NEXT?
Stoke v Watford (Barclays Premier League, Saturday October 24)
Arsenal v Bayern Munich (Champions League, Tuesday October 20)
Source : PA
Source: PA