Mauricio Pochettino’s side took the lead early on at St. James’ Park, as Jan Vertoghen forced the ball home from close range.
But Joselu equalised for the Magpies within a couple of minutes, heading home Matt Ritchie’s pinpoint centre.
With 17 minutes on the clock, though, Spurs led once more through Dele Alli’s back-post header.
And though Newcastle fought hard for an equaliser, with debutant Salomón Rondón hitting the woodwork late on, that goal from England midfielder Alli proved to be the winner as Spurs emerged with the victory.
A restless opening quarter of an hour began with Ritchie blazing high and wide, before Mo Diamé’s error gave Lucas Moura a sight of goal which Ciaran Clark did well to snuff out.
But with barely eight minutes on the clock, Spurs seized the advantage. Christian Eriksen’s corner was flicked on by Davinson Sanchez, with Vertonghen poised at the far post. He helped it goalwards with his head and, despite the best efforts of Martin Dúbravka, the ball crossed the line.
It took United just two minutes to respond. Ritchie whipped in a fine inswinging cross from the right and, with the visitors’ defence bypassed, Joselu stole in to glance a header past the helpless Hugo Lloris to pull the hosts level.
In keeping with the pace of the game, though, they were only level for seven minutes. Serge Aurier sent over a cross from deep on the right and it was met by Alli, who nodded the ball back across Dúbravka and into the far corner.
Paul Dummett flashed a shot past the post as Benítez’s men rallied again but Spurs, with Eriksen’s dead ball delivery, remained a threat, and Sanchez nodded just wide from another set piece. At the other end, Clark volleyed a high, hanging ball back across goal, but Kenedy couldn’t quite connect at full stretch.
Within two minutes of the restart, the Magpies almost had an equaliser. Jonjo Shelvey won his header, with the ball looping over the defence into the path of Diamé. His left footed effort was well-struck, but the ball cannoned back off the post.
Another opportunity followed a few minutes later. Joselu produced a wonderful through ball with the outside of his right foot, which split the Spurs defence and found Kenedy. But the Brazilian, with Lloris racing off his line, couldn’t get a shot away quickly enough.
Dúbravka then denied former United man Moussa Sissoko, saving low to his left, before Benítez deployed his new number nine Rondón from the bench.
And the Venezuelan frontman made his presence felt, connecting with fellow substitute Christian Atsu’s cross, but Lloris held it comfortably.
United’s final roll of the dice saw Benítez introduce Yoshinori Mutō for the final ten minutes and the hosts continued to push. They were inches away from drawing level again with five minutes remaining as Rondón took aim, but his shot was deflected onto the crossbar with Lloris stranded and the visitors held on to claim the points.