Goals from Dean Cox and Lloyd Owusu put the Seagulls in charge in the first half, and they clinched victory with 10 men after defender Andy Whing was sent off for two bookable offences late on.
Oldham were much improved after the break and substitute Lewis Alessandra crashed in a 62nd-minute goal, but Owusu struck again only two minutes later to secure maximum points.
Winger Cox broke the deadlock by heading in an Owusu cross at the far post in the 26th minute - and Owusu doubled the advantage nine minutes before the break with a misdirected header which went in off veteran keeper Mark Crossley.
Alessandra brought on a spell of Oldham pressure by firing home in a one-on-one situation with keeper Michel Kuipers.
But Owusu had the final say by cashing in on defensive hesitancy to fire his fifth goal since joining the Seagulls on loan from Cheltenham.