The Seagulls had previously failed to get the better of their opponents on Welsh soil on nine occasions prior to this afternoon, losing six and drawing three of those encounters, but Glenn Murray's first-half finish ended that barren run.
Three points for Albion is enough to lift them into ninth place in the Premier League table, while struggling Swansea - with just four points from their last eight games - drop into the relegation zone.
Brighton, showing no changes on the back of their draw at home to Southampton last weekend, had to dig in defensively in the early stages as the Swans quickly came out of the blocks.
The hosts struggled to create too much in front of goal, though, and it took until 29 minutes into the contest before the first serious attempt arrived at either end.
A pivotal strike it proved to be, too, as Murray bundled the ball over the line after being picked out by Anthony Knockaert's left-footed cross for the only goal of the match.
While the finish may have been scruffy, Brighton cared little and it was they who found themselves on top for the remainder of the first half, coming close to a second when Lewis Dunk tested Lukasz Fabianski with a powerful header.
Fresh on the back of his England call-up earlier this week, Swansea striker Tammy Abraham was frustratingly cut off from the rest of his teammates as the home side failed to register a shot all half.
Abraham could not get the better of Mathew Ryan from that rare opening, while a goalmouth scramble soon after ended with the ball staying out of the net, leading to the home fans growing more and more frustrated as the hour mark approached in South Wales.
Albion did not come under too much pressure in the remainder of the match, either, as Swansea - despite chasing the game for all of an hour - mustered just that one serious effort heading into extra time.
There was to be one late chance for City to snatch a point, though, with Abraham threading the ball through for substitute Luciano Narsingh, who failed to keep his attempt down and struck the crossbar from the last meaningful act.
Brighton saw out the remaining seconds to earn back-to-back away wins in the top flight for just the second time in their history.