Mauricio Pochettino's men had second-half goals from Dele Alli and Ben Davies to thank, as Spurs made use of the dismissal of Jonjo Shelvey for a stamp on Alli in order to claim three points on the road.
Newcastle arguably started as the better of the two sides and Dwight Gayle caused some early issues as he spun Toby Alderweireld, before skewing a volley over the crossbar without troubling Hugo Lloris.
Spurs were unable to find a rhythm for much of the first half, largely thanks to United's impressive industry, leaving Christian Eriksen to try his luck from distance with an effort that was saved down low by Rob Elliot.
Christian Atsu grew into the game for the hosts and he caused a few issues down the left, although Spurs youngster Kyle Walker-Peters provided some important pace to prevent the Ghanaian from causing too many problems.
In a first half that proved to be more intriguing than entertaining, Eriksen tried his luck again from distance, this time bending a curling effort towards the far post that a diving Elliot saved comfortably.
The game was turned on its head after the break, however, when Shelvey was given a straight red card for an off-the-ball stamp on Alli, handing Spurs what turned out to be a decisive numerical advantage.
It did not take too long for the visitors to make the required breakthrough, as Eriksen picked out Alli with a memorable ball in behind the defence, leaving the playmaker to break free and prod beyond Elliot.
The goal seemed to kick Spurs into action and the rise in tempo soon saw Pochettino's men double their lead, Eriksen and Alli combining again with a neat one-two which left Davies with the chance to stroke past the Newcastle keeper.
United sought to push for a route back into the match in the final 10 minutes, although it proved too little too late for Benitez's men as Spurs closed out the game to earn three opening points.