Shkodran Mustafi opened the scoring with a brilliant header off a Mesut Ozil in the 8th minute, and the Gunners should have extended the lead further with clear-cut chances for both Pierre-Emerick Aubameyang and Ozil.
Wenger made six changes to the side that beat AC Milan on Thursday night in the San Siro.
Despite the meagre numbers the biggest cheer heard in these parts for months erupted when Deeney had that second-half penalty saved by Petr Cech. In the first situation he showed a lot of humility. It also shows remarkable intelligence because without remarkable intelligence you don't last in the game, because you have to deal with so many different problems.
Wenger, who was the subject of intensifying scrutiny over his future following four consecutive losses - including the Carabao Cup final against Manchester City - and underwhelming performances, suggested the tanker of despair had begun to turn.
However, Ozil wouldn't be denied his 50th EPL assist for long.
Speaking specifically about Cech's clean sheet record, Wenger praised the 35-year-old for his ability to stay at the top over the course of his career.
"I told you before the game that for us the desire is to win the game no matter what people say". "We controlled the game in the first few minutes but the second goal was very, very hard for us". "We have still some work to do, but we are on a good way".
"I always try to deliver my best in every game as I hope that the team achieves something this season", he added.
The Watford skipper, who accused Arsenal of lacking cajones in the wake of Watford's 2-1 win against them earlier this season, was faced by fierce jeers in the build up to the effort.
Henry has coached the likes of Eden Hazard and Kevin De Bruyne in the Belgium set-up and Arsenal's key players are convinced the former Gunner can help them rediscover their form.
Watford play in the Premier League next Saturday with a trip to Liverpool (17:30 GMT).