First-half goals from Callum Wilson and Miguel Almirón proved decisive despite Harry Kane's header for the North London outfit, who remain third but are now just two points ahead of Eddie Howe's in-form United.
Newcastle were able to call on Bruno Guimarães after the Brazilian midfielder's partner, Ana, gave birth to the couple's first son, Matteo, on Friday, while Joe Willock replaced Jacob Murphy in the only change to the starting XI from the last two games.
The home side, who had won all five of their previous matches at the Tottenham Hotspur Stadium, started well, with Heung-Min Son seeing a shot fielded by Nick Pope inside the opening minute after a strong run before the South Korean star sent another effort curling inches over two minutes later.
Newcastle had loud appeals for a penalty in the fourth minute, when Joelinton - whose first Magpies goal came on this ground in August 2019 - brought down a beautiful Fabian Schär pass and Emerson Royal's clumsy attempt to win the ball saw the United man go down but referee Jarred Gillet waved play on, and Almirón's shot was deflected behind.
Pope made a fantastic save in the 11th minute, when Son beat the offside trap and raced onto Kane's pass only to see the Newcastle netminder throw up a big hand to block before Kieran Trippier cleared.
Eric Dier gave Hugo Lloris a huge scare when his overhit backpass went just wide, with the French goalkeeper scrambling, and the resulting corner was half-cleared as far as Almirón, whose half-volley was well off target.
In the 23rd minute, Schär did well to get in the way of a Ryan Sessegnon shot, then two minutes later, at the other end, Trippier pumped in a free kick which was nodded across goal by Sven Botman and met by Wilson, but his shot was collected by Lloris.
Pope made his second big save of the afternoon just before the half-hour mark, keeping out Kane's strike with an outstretched left leg after the England captain had ran from his own half - and two minutes later, the visitors were ahead.
Lloris came out of his box to deal with a ball over the top from Schär, but collided with Wilson who, aware that the goalkeeper was some way off his line, lofted the ball into the empty net with a superb finish. There was a VAR check, but the goal stood - and it was 2-0 in the 40th minute, as Sean Longstaff won the ball from a Spurs goal kick.
Almirón burst into the box, shrugging off Sessegnon and bamboozling Clement Lenglet then, with a cool finish from a narrow angle, scored his sixth goal of the season and his fifth of an increasingly remarkable month for the Paraguayan.
Torrential rain began to fall at half time, with some thunder and lightning for good measure, and Newcastle knew that they would have a storm to weather at the beginning of the second period.
They felt they should have had a penalty in the 52nd minute, when Joelinton's header hit the arm of Royal, but a corner was awarded instead and Schär had an effort palmed away by Lloris.
In the 54th minute, the hosts controversially pulled one back when Kane stooped to head home from a corner, with a lengthy VAR check for offside eventually going in favour of the home team.
Front-foot defending from Schär - outstanding on his 100th Premier League appearance for United - resulted in him dispossessing Son and testing Lloris before Pope was called into action in the 69th minute to hold a shot from substitute Ivan Perisic.
United, though, rarely looked in serious danger of conceding an equaliser, managing the final stages - including five minutes of added time - with the minimum of fuss to reward their magnificent travelling supporters with a second win in the capital this month.
