Nacho Monreal put the Gunners ahead early on when he shot through a crowded penalty area after Brighton had failed to clear a free-kick.
A well worked Brighton free-kick resulted in Solly March striking the post from 20 yards shortly afterwards.
But Arsenal added a second goal after half-time when a slick passing move on the counter-attack was emphatically finished off by Alex Iwobi.
The win ensures Wenger’s side is a point behind north London rivals Tottenham in the chasing pack behind Premier League leaders Manchester City.
Brighton became the 45th different club that Wenger has defeated in the Premier League – more than any other manager in the competition’s history.
After an impressive September, in which the Gunners went unbeaten with five victories and a draw in all competitions, they began the month of October with a dominant victory and performance.
For the first time in Wenger’s Arsenal tenure he has had to juggle the different challenges posed by the Europa League but the erudite Frenchman appears to have got a handle on the requirements of playing on Thursday and Sunday.
Indeed, against newly promoted Brighton the Gunners looked something akin to the flat-track bullies of old. While not at their brilliant best, it was a display with the swagger and fluid football which has become Wenger’s trademark.
This was epitomised by Arsenal’s stylish second goal 11 minutes after half-time, which was a thing of beauty; a swift interchange of passes involving Aaron Ramsey, Alexis Sanchez and Alexandre Lacazette left Brighton’s players in a spin before Iwobi fired home.
The acid test for Arsenal will come against their rivals for the top four, but there at least appears to be growing momentum and belief about Wenger’s side.