Younes Kaboul’s shot on 10 minutes took a deflection off Aaron Ramsey and nestled into the bottom corner.
Etienne Capoue’s shot was pushed into the path of Deeney, who struck home to double the visitors’ advantage.
The hosts rallied and pulled one back through Alex Iwobi and came close to levelling the game when Lucas Perez's shot crashed off the crossbar.
Walter Mazzarri's side managed to hold off the relentless pressure and secure their first Premier League win of 2017.
The Hornets came into the game having crashed out of the FA Cup at the hands of League One Millwall, but started in fine fashion against the Gunners.
Watford go two-up early on
Ramsey struck over with the first chance of the game before the visitors broke the deadlock on 10 minutes.
Tom Cleverley rolled the free-kick to Kaboul, who lashed the ball into the bottom corner via a deflection off the back of Ramsey.
Watford had soon doubled their lead, and deservedly so, when Capoue burst forward from the halfway.
The midfielder’s shot was saved well by the oncoming Petr Cech, but the ball was pounced upon by Hornets skipper Deeney, who made no mistake with the rebound from close range.
Hornets dominant in first-half
Mazzarri’s men were showing were giving the travelling supporters something to cheer about throughout the first half and could have added to their lead.
Capoue forced a low save out of Cech before the playmaker crossed for Sebastian Prodl, whose header was tipped over the bar by the Arsenal shot-stopper.
Daryl Janmaat stung the gloves of Cech with a fierce effort 11 minutes before the half, but the hosts failed to have a shot on target in the first 45 minutes.
Hosts rally and pull a goal back
The Gunners started the second-half quickly and they had two brilliant openings inside the first five minutes.
Half-time substitute Theo Walcott flashed wide of goal before Mesut Ozil helped the ball on to the wide man, who forced Heurelho Gomes into making a fine save low down.
Arsene Wenger’s side continued the relentless pressure and after Gomes denied the hosts a further time when he stopped Ozil’s effort, they pulled one back in the game.
Mazzarri's side survive late scare
Alexis Sanchez eased past his man before hanging the ball up to the back post and Iwobi struck back across goal and into the net.
Watford frustrated their opponents for a period of time and the hosts’ next opening didn’t come until eight minutes from time.
Nacho Monreal struck over despite a clean connection with the ball before the Gunners came within inches of finding an equaliser.
The Hornets were almost undone by a simple throw-in, and Perez thrashed his shot off the crossbar to the delight of ‘keeper Gomes, who was well beaten.
Mazzarri’s side managed to hold on despite the relentless pressure for their first three points since the turn of the new year.