Alli showed his aerial prowess as he steered a fine first-half finish across Martin Dubravka to seal the points for Spurs.
It concluded a frantic opening to the match, where Joselu's 11th-minute header cancelled out a Jan Vertonghen effort that was shown to be nine millimetres over the line by the Goal Decision System.
Mauricio Pochettino's Spurs were rarely at their fluent best — fatigue possibly a factor for five FIFA World Cup semi-finalists in the starting XI — and Mohamed Diame and new signing Salomon Rondon were denied by post and crossbar as Newcastle chased a second equaliser in vain.
With all eyes on Harry Kane's bid to end his August goal drought that now stands at 14 Premier League matches, it was Tottenham's centre-backs who combined for the game's opening goal.
Davinson Sanchez flicked on Christian Eriksen's right-wing corner for Vertonghen to score, despite the best efforts of Dubravka.
The Spurs defence soon had a moment to forget, however, when Joselu pulled around the back of Sanchez to dispatch Matt Ritchie's superb delivery from the right.
It was three headed goals in 18 minutes when Serge Aurier picked out Alli at the far post from deep on the right flank.
Rafael Benitez's side was almost level in the 48th minute.
Diame was afforded room in the box to clatter a left-footed shot against the upright, while Alli should have done better at the other end when picked out by another delightful Eriksen ball.
Kenedy's heavy 51st-minute touch allowed Hugo Lloris to preserve Spurs' lead before opposite number Dubravka showed lightning reactions to deny ex-Newcastle man Moussa Sissoko.
More unconvincing set-piece defending left Lloris thwarting Ayoze Perez at close quarters and Tottenham just about hung on after Vertonghen deflected an effort from substitute Rondon against the crossbar.
Newcastle will attempt to get its season up and running at newly promoted Cardiff City next weekend, while Tottenham will play a home match at Wembley for the final time when it hosts Fulham.