Pierre Emerick Aubameyang and Henrikh Mkhitaryan each contributed a goal and an assist after Shkodran Mustafi's header had given the Gunners an early lead in a clinical attacking display at the Emirates Stadium in London.
Watford came back stronger in the second and Arsenal looked as if they would struggle to maintain their lead, but a goal from Aubameyang followed a penalty from Troy Deeney which was saved by Cech, his first penalty save in 16 attempts as an Arsenal player.
"We had a disappointing period and our supporters suffered like we suffered", said Wenger. "But our job is to perform and stick together in important moment and get the fans back on side".
The victory did little to alter the view of former Tottenham manager Tim Sherwood
Mesut Ozil: Another masterclass from the German who became the quickest to 50 clean sheets in the Premier League. The Europa league seems to be the only glimmer of hope for a piece of silverware, and a way into the champions league for Arsenal.
But it was the Watford skipper's own bottle which was called into question at the Emirates as he saw a second half penalty saved in a routine win for the home side. They have 36 points from 30 matches and, on this evidence, should have enough quality in their squad to ensure another season of Premier League football.
"I think the team did very well and we are all happy, we are feeling better of course".More news: Real Madrid coach Zinedine Zidane reveals captain Sergio Ramos' embarrassing situation
'When I was in Dortmund, I was playing every three days but now I play once a week or have a long time between games.
The Gunners were reminded of his comments before the game and Wenger says they were a factor. I didn't play a lot in January so it was hard to find a rhythm. The save helped the Czech stopper achieve his 200th clean sheet in the Premier League.
Aubameyang has walked into the Wenger Out saga and he was asked whether the manager was taken for granted.More news: Two deadly March home explosions could be related, police say
Watford took off Femenia and replaced him with Will Hughes, and moments later Arsenal could have had a penalty when Adrian Mariappa clattered Mkhitaryan as he crossed but the referee waved play on as the ball just eluded Aubameyang in the middle.
Prior to their midweek 2-0 away win over AC Milan in the Europa League, the Gunners had lost four games in a row in all competitions, including back-to-back 3-0 drubbings by runaway Premier League leaders Manchester City.More news: EU Extends Anti-Russian Sanctions Over Ukrainian Territorial Integrity Breach