Florin Andone got the all-important winner, heading in a cross from Anthony Knockaert after ghosting in front of Philip Billing with 11 minutes remaining.
It capped a much improved second half effort from the Seagulls, who before today were the only team in the top four divisions without a league win since the turn of the year.
Jonas Lossl had made two stunning saves in the build-up to what proved to be the winner and Billing had cleared a Shane Duffy header off the line, so Town could have few complaints as their run without a goal away from home was extended to 452 minutes.
The first half had been something of a non-event. It took more than half an hour for the first shot on goal, while Alireza Johanbakhsh crashed an effort against the crossbar
Brighton stepped things up after the restart and were rewarded when Andone netted from close range.
The closest Town went to ending their barren scoring run on the road came when Steve Mounie headed a Florent Hadergjonaj cross firmly only for Mat Ryan to tip over.
Brighton’s goalkeeper had also got down smartly to deny Alex Pritchard on the stroke of half-time but the Seagulls were worthy of the win over the 90 minutes.