The League Two outfit were never seriously troubled at Sixfields by a Seagulls side who were reduced to 10 men late in the first half by the dismissal of Matt Sparrow. And although they showed more intent in the second half, the visitors were never able to claw back the two-goal deficit.
Michael Jacobs, 18, grabbed the opening goal on his full debut as early as the 12th minute when he cut inside before beating Michael Poke from 15 yards.
Six minutes later Billy McKay doubled Northampton's advantage with a diving header at the far post from a pin-point cross from the impressive Ryan Gilligan.
Sparrow was shown a straight red in the 35th minute for hitting out at Abdul Osman and Brighton never really recovered.
The Cobblers should have increased their advantage in the second half with skipper Andy Holt heading over from Nathanial Wedderburn's cross, while the latter went close himself with a diving header.