Danny Welbeck's smart first half finish put the hosts in front at the break, but Nick Woltemade's superb backheel - his fifth goal since his summer move to St. James' Park - drew Eddie Howe's men level at the Amex Stadium.
But veteran frontman Welbeck's 84th-minute winner made it another joyless trip to the home of the Seagulls, with Newcastle unable to respond for a second time.
United were first to threaten in a flowing, open first half. Captain Bruno Guimarães feinted inside after latching on to Sandro Tonali's headed knockdown in the box, but skewed his shot just wide of the right-hand post.
The hosts' former Newcastle man Yankuba Minteh was lively early on, as he had been in the matches between the two sides last term. Guimarães did well to stop the Gambian international shooting after cutting inside before Georginio Rutter twice tested Rutter; his second attempt, angled towards the bottom corner after Joelinton had given the ball away cheaply in the build up, required a strong hand to turn it past the post.
At the other end, Sven Botman nodded well wide after meeting an Anthony Gordon cross but just before the break, the Seagulls cut through the visitors' backline to break the deadlock. Attacking down the middle, Rutter drove forward and slipped a neat through ball between Malick Thiaw and Sven Botman for Welbeck to run onto and dink a finish over the advancing Pope.
The half closed with Woltemade, in fine form for club and country heading into the contest, heading Tonali's free kick over in what looked like the Magpies' clearest chance of the opening 45. But after the restart, Brighton began to apply considerable pressure. Yasin Ayari curled wide after Minteh, Ferdi Kadıoğlu and Welbeck combined to present him with an opportunity, and Maxim De Cuyper lashed an effort towards goal after Thiaw's clearance fell for him that needed Pope's firm intervention to stop his side going two down.
Newcastle upped the intensity around the hour, with Gordon cutting inside and firing wide having picked up a pass from substitute Lewis Miley, while Guimarães saw a powerful drive charged down. The Brazilian international then picked out another substitute, Jacob Murphy, with a smart lofted pass over the Brighton defence, but the winger, off-balance, lifted his shot way over the crossbar.
With just over quarter of an hour left, United went close again as Guimarães did brilliantly to turn Kadıoğlu in the box and fire in a shot which Bart Verbruggen repelled. But just a few minutes later, Howe's charges did draw level, and in some style. Miley's cutback was precise but Woltemade's finish, nonchalantly flicked right into the bottom left-hand corner, was magnificent.
Guimarães almost added a quickfire second but saw his shot deflected over from close range after Verbruggen failed to adequately deal with Dan Burn's long throw. They were made to pay, devastatingly, inside the final ten minutes when Ayari found Mats Wieffer on the edge of the Newcastle box. Burn's sliding challenge stopped the midfielder from getting his shot away but the loose ball fell fortuitously for the oncoming Welbeck, who whipped home his second.
It proved to be the winner. Woltemade had a late chance to level once more but missed his kick after Murphy nodded a cross back into his path, while Burn was a whisker away from connecting with a Botman flick in front of goal. United's wait for a Premier League victory at the Amex continues.
