A fascinating first-half seen both teams go very close to opening the scoring.
Newcastle first of all thought they had, when Joselu rose highest to prod a header towards the far post, only for Lukasz Fabianski to deny him with a marvellous save.
The home side then went close through Jordan Ayew, who's powerful shot was saved by Rob Elliot, and Alfie Mawson, who's header crept just wide of the post.
Both teams also had penalty claims waved away in the first 45 minutes. First, Mikel Merino danced through the Swansea defence, and looked to have been brought down, although the replay showed the Spaniard had dived just outside the box.
Jamaal Lascelles then attempted a diving headed clearance, only for him to land on the ball chest-first.
Tom Carroll was presented with a good chance when he crept in behind the away defence, but could not find the net from a difficult angle.
Isaac Hayden looked to put his side into the lead just before half-time, but his well struck shot was straight at Fabianski, who did well to hold onto the ball.
The second half began and controversy struck. Matt Ritchie, running onto a pass from Merino, raised his foot high in an attempt to get to the ball. Mawson could have been injured, but only a yellow card was awarded.
The first big chance arrived when Leroy Fer slipped a ball through the back-line for Tammy Abraham, who rounded the keeper, but had his shot cleared off the line by Jamaal Lascelles.
Ayoze Perez found himself played in from the right, but struck a very tame shot straight at Fabianski. The Spaniard should have done better.
The game rather fizzled out for the next ten minutes, but then burst into life when Wilfried Bony was introduced. The atmosphere was cranked up a notch and the intensity increased.
The visitors weathered the storm, and then hit the Swans with the sucker punch when Lascelles rose highest to meet Ritchie's corner from the left. 0-1.
From then on, Newcastle were forced to sit back and defend their lead.
Swansea did not really offer much threat going forward. Substitute Luciano Narsingh come closest to grabbing their equaliser, but his strike was saved by the legs of Rob Elliot.
A set-piece barrage was to come, but the Newcastle defence held out and went on to secure their first away victory of the season.
That makes it six points from twelve for Newcastle United. After the negativity of the transfer window, and doubts surrounding Benitez's future, this is exactly what they needed.