A second-half goal from Tomer Hemed proved decisive as Chris Hughton's team registered their second top-flight success of the campaign, as well as ending Newcastle's three-game winning streak in the process.
Newcastle could have opened the scoring as early as the second minute when Mikel Merino met a corner on the edge of the area, but goalkeeper Mathew Ryan made an impressive save to his right to prevent the volley from finding the bottom corner.
Up the other end, Brighton pressed forward at will but two opportunities for Hemed failed to result in a goal, with a header being directed over the crossbar and a 25-yard strike going too close to Rob Elliot.
Moments later, Pascal Gross had the opportunity to volley home from eight yards after Solly March's cross had deflected into his path, but the German's goalbound volley struck teammate Anthony Knockaert and went wide of the post.
Midway through the first half, Newcastle should have gone ahead through Joselu but despite a smart turn inside the penalty area, the summer signing dragged his effort wide of the post from close range.
Newcastle were beginning to dominate the play and shortly after the half-hour mark, Ayoze Perez could have netted his first goal of the season, only to direct a first-time effort over the bar from 12 yards.
Chances were few and far between as the first half drew to a close but within six minutes of the restart, Brighton got their noses in front thanks to Hemed.
A clever free kick found Dale Stephens at the back post and after his header across goal found Hemed, the forward did the rest with a hooked finish into the roof of the net.
Brighton were in the ascendancy and should have probably added to their tally soon afterwards when March met Bruno's cross at the back post, but Elliot pulled off an almost miraculous save with his boot to keep Newcastle in the game.
However, after the hour mark, Newcastle finally started to press in search of an equaliser and the North-East outfit almost found it when Merino's 25-yard strike was deflected just wide of the post by the head of Shane Duffy.
Jonjo Shelvey was introduced into the action to add a creative spark and soon after his arrival, the midfielder struck the post with a corner with Ryan sprawling towards his near post.
Newcastle threw men forward in the final stages but aside from a weak stoppage-time effort from Dwight Gayle, the Magpies did not trouble their hosts who held on for what may prove to be a crucial win come the end of the season.