Arsenal are sixth in the table with 48 points, 12 behind the last Champions League qualifying spot.
Wenger made six changes to the side that beat AC Milan on Thursday night in the San Siro.
Arsenal's record signing Aubameyang relieved the pressure on himself on the hour-mark after rounding Karnezis to poke into an empty net following a through ball from Henrikh Mkhitaryan.
The victory was finally sealed 13 minutes from the end, when Aubameyang set up Mkhitaryan for his first league goal in an Arsenal shirt.
The Hornets' best chance of the game fell to captain Deeney after Pereyra had been fouled in the penalty area by a combination of Ainsley Maitland-Niles and Alex Iwobi.
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And that's exactly what happened as they ran out 3-0 winners with Petr Cech saving a second-half spot-kick from Deeney.
We may have lacked a bit of freshness, but at least we showed some cojones again!
"They all just backed off".
"I didn't see it myself but I did have that confirmed, which was part of the reason why the people in the directors' box had to go inside to save any more problems like that".
Cech came to Arsenal's rescue on the stroke half-time as he produced a fine save at his near post to keep out Richarlison's header to enter the break still leading. They attacked well in the first half, and an eager Ozil looked frustrated at times as he failed to make anything of a couple of decent chances, at times hindered by the quality of passing from his team-mates.
"We suffered a bit at the start of the second half but after that with our spirit, we stuck together and in the end it was a convincing win", he said. I wouldn't go so far as saying it was a flawless performance.
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Silva has been sporadically absent for Premier League matches as he regularly returns to Valencia to be with his family. Hopefully, the players will come back safe - without injuries - and we will go to Everton and the quarter-finals.
Cech, without a league clean sheet since December 16, did well to prevent Abdoulaye Doucoure sweeping home a quick reply.
"He had to wait a while to save a penalty, and it's quite fortunate that it's against Deeney", added Wenger.
The win marked several landmarks for Arsenal.
The Czech Republic and former Chelsea 'keeper also saved a penalty on his way to bringing up a 200th EPL clean sheet over the last 14 years. The German was left relatively unchallenged as he was able to bag Arsenal's 1000th Premier League goal at home.
Watford have now lost all five of their away Premier League matches in the month of March.
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The Gunners secured their first Premier League win in four games to continue their recovery from a disastrous run of results.