More than 6,000 travelling supporters celebrated at the final whistle as a Dan Ballard own goal and a brace from Alexander Isak proved the difference between the two sides.
Ballard diverted a low cross from Joelinton past Anthony Patterson in the first half, then Isak took advantage of a defensive error in the second before converting a late penalty, but the Magpies were dominant throughout at the Stadium of Light.
Ultimately, clear-cut chances were always likely to be few and far between in such a hard-fought fixture, but Eddie Howe's men could have taken the lead in only the second minute when Kieran Trippier - back in the side after missing the New Year's Day defeat at Liverpool through injury - crossed for Sean Longstaff, but his header was unorthodoxly kept out by Patterson, the Black Cats goalkeeper.
Trippier then saw a free kick deflected into Patterson's arms and Longstaff fired over in the 22nd minute after connecting with a Trippier cutback.
Maybe Ballard was fortunate to stay on the pitch when Isak burst through on goal before going down under the defender's challenge on the half-hour - referee Craig Pawson waved away United appeals for a foul - but he could consider himself unlucky five minutes later when he turned Joelinton's cross into his own net after strong work from the Brazilian on the left. Isak would surely have tapped home but for the defender's intervention.
Half time was approaching when an acrobatic effort from Miguel Almirón went just wide. But a matter of seconds after the break, Almirón picked the pocket of Pierre Ekwah just outside the box and unselfishly squared for Isak to double United's advantage and spark wild celebrations behind the goal housing the Newcastle support.
Wearing black and white shirts, white shorts and white socks, the Magpies were starting to feel at home at the stadium of their fiercest enemies - although Martin Dúbravka had to be alert to keep out Ekwah's strike in the 48th minute.
Then Alex Pritchard sent a dipping effort narrowly over the bar. In the 68th minute, Luke O'Nien bravely blocked an Almirón shot before Dúbravka denied Pritchard.
Late on, Gordon flashed an effort across goal before, with two minutes left, he was fouled in the box by Ballard and Isak stepped up to wrap up the scoring, and Newcastle United's first Tyne-Wear derby win in 12 years - a feat marked with a celebratory team photo on the Stadium of Light pitch after the final whistle.