Nigerian global Alex Iwobi doubled the hosts lead by crashing an effort into the net following a sensational back-heeled pass from Alexis Sanchez to seal the three points for the Gunners and send them into this worldwide break in positive spirits.
But Wenger, who was celebrating his 21st year at the club, admitted afterwards that his side could have been more clinical.
The Nigerian worldwide, who was a major doubt for the Gunners clash, finished off a backheeled assist from Alexis Sanchez in the 56th minute after Nacho Monreal had shot Arsenal into the lead in the 16th minute.
Arsenal's sixth win from their last seven matches in all competitions moved them to within six points of leaders Manchester City heading into the global break.
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"It was a hard week because the game at Bate (Europa League matchday 2 clash on Thursday) was a hard game".
"I'm going to have to go with Jurgen Klopp's men as on paper they are the much better side". I knew that after the game at Liverpool, everybody did write us off.
Meanwhile Brighton manager Chris Hughton added: "It was a spirited performance".
"He is the kind of player who has good availability, helps you a lot to get out of pressure and creates spaces".
"Nothing is permanent. You aren't bad in a permanent way if you can do something about it, and you are not good in a permanent way if you don't keep your urgency".