Despite Newcastle's struggles on the road, they had a chance to take the lead early on when Bruno Guimarães' shot from inside the area went wide of the post.
The hosts were the stronger team in the first half, coming close to taking the lead when Georginio Rutter's effort from the edge of the area was saved by Nick Pope.
Brighton eventually broke the deadlock four minutes before halftime when Rutter's through ball played Danny Welbeck in, and the striker scored with a chip over Pope from just inside the area.
Although Brighton continued to press, they were wary of their recent struggles to keep clean sheets at home, having kept just one in their last 19 Premier League games.
The visitors didn't create much pressure, and Brighton could have doubled their advantage shortly after halftime, but Yankuba Minteh's pass found Yasin Ayari in the area, and his shot went wide of the post.
Newcastle's poor record against Brighton, with just 13% win rate prior to kickoff, suggested it wasn't their day.
However, the Magpies equalized in the final 15 minutes, as Nick Woltemade scored with a stylish finish from inside the area.
Despite the momentum shift, Brighton claimed the win six minutes from time, as Welbeck collected a loose ball and scored with a shot into the bottom left corner, securing a victory that lifts them three places to ninth, while Newcastle drop a place to 12th.