The Gunners arrived in Hertfordshire on the back of a wretched run on the road in the league with just two wins in 12 away games since the start of December.
Watford came into the match on a high after their stunning comeback from a two-goal deficit at Wembley to defeat Wolves 3-2 after extra-time and book a FA Cup final place against Manchester City next month.
However, it was the Gunners who had a dream start when Pierre-Emerick Aubameyang opened the scoring inside the opening 10 minutes in farcical circumstances thanks to a howler from Watford goalkeeper Ben Foster.
Javi Gracia’s side were then left with a mountain to climb moments later when their skipper Troy Deeney was sent off for violent conduct.
Despite being a man down, Watford pushed Arsenal all the way for the remainder of the game as the north Londoners hung on for a slender win and first clean sheet of the season to move them back up to fourth on goal difference ahead of Chelsea.
The Hornets remain down in 10th on 46 points.
Foster, Daryl Janmaat, Christian Kabasele and Adam Masina came in to replace Heurelho Gomes, Adrian Mariappa, Roberto Pereyra and Jose Holebas in four Watford changes to the XI which started last weekend's FA Cup semi-final win.
Bernd Leno, Henrikh Mkhitaryan, Alex Iwobi, Shkodran Mustafi, Konstantinos Mavropanos and Granit Xhaka were all handed starts as Arsenal boasted six changes to Thursday's 2-0 win against Napoli in the Europa League quarter-final first leg at the Emirates Stadium.
Watford controlled the early moments of the game only to concede the opening goal out of the blue in the 10th minute when Foster dwelled on the ball inside his own area and his subsequent clearance rebounded into the net off Aubameyang who had quickly closed him down.
Things went from bad to worse a minute later when Deeney seemed to aim an elbow into the side of Lucas Torreira’s face as he ran past him and it was spotted by the assistant referee, which resulted in Craig Pawson issuing a straight red card.
Despite being at a numerical disadvantage, Watford almost levelled on 20 minutes when Craig Cathcart hit a close-range half-volley at goal which Bernd Leno did well to save with his legs.
The Hornets continued to press, but they were almost caught out on 26 minutes when a quick break resulted in Iwobi’s strike being acrobatically pushed behind by Foster.
Back came Watford with a free-kick which former Tottenham man Etienne Capoue curled over the defensive wall only to be denied by Leno who tipped the ball wide at full stretch.
Arsenal finally started to use their extra man in the opening stages of the second half and they should have extended their lead on several occasions.
On 52 minutes Aubameyang was inches away from diverting Iwobi’s low ball across the area into the net from close range, before Foster produced a superb prevent Mkhitaryan’s side-foot volley at the back post from finding the back of his net.
Mkhitaryan had another two opportunities to try and test Foster but got his shots horribly wrong as the Hornets clung on.
The hosts then went close to an equaliser out of nothing just after the hour when Masina got a sight of goal from 30 yards and watched as his fierce strike beat the dive of Leno but crashed back off the crossbar.
Watford continued to throw men forward in search of an equaliser and they were almost caught on the counter-attack again on 74 minutes when Mkhitaryan got space down the right and put a low cross into the middle towards Aubameyang who could only divert his shot wide of the front post.
Andre Gray thought he had got the ten-men level in the 80th minute when he managed to take the ball past Leno inside the area, only for Ainsley Maitland-Niles to block his angled effort towards the empty net.
Three minutes later, Janmaat did well down the right and put a teasing cross towards the back post where Will Hughes could only guide his header over the top.