Alli showed the aerial prowess that booked a World Cup semi-final spot for England last month as he steered a fine first-half finish across Martin Dubravka.
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 the five World Cup semi-finalists in his 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 were 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.
32 - Spurs have never lost a Premier League fixture in which Dele Alli has scored, winning 26 and drawing six of the previous 32 games he has netted in. Impact. pic.twitter.com/FpJQftYAZI— OptaJoe (@OptaJoe) August 11, 2018
What it means: Pochettino's faith in stability passes early test
Despite fan concerns over Tottenham's lack of activity during the transfer window, Pochettino's settled side are under way in their bid to continue the fine form that has brought top-three finishes in each of the past three seasons. Spurs can lift their performances a few levels above what they produced in the north east of England; how often Newcastle can perform in such a combative manner will have a key influence over their survival hopes.
Pat on the back: Eriksen excellence a delight
In a game marked by frantic periods of action and errors, Tottenham's Denmark playmaker was a cut above. Perhaps assisted by his country's World Cup absence, Spurs were spared sustained worries over Eriksen's future. As usual, he was their creative inspiration, supplying five key passes over the 90 minutes.
Boot up the backside: Kane's August woes continue
The novelty of Kane's run without a goal in the Premier League season's opening month stretching to 14 matches will not concern Pochettino greatly. However, the sight of his star striker lacking sharpness and ceding possession with heavy touches and poor passes might. This was a tired performance from the World Cup Golden Boot winner.
Key Opta Stats:
149 - There were just 149 seconds between Spurs opening the scoring and Newcastle drawing level through Joselu. Action. pic.twitter.com/x8SWUets3P— OptaJoe (@OptaJoe) August 11, 2018
- Tottenham defender Vertonghen's goal was his first in 161 Premier League games, since netting against Swansea in March 2013.
- Kane has never scored a Premier League goal in August, despite playing 14 games, 988 minutes and attempting 46 shots.
- The first three shots on target in this match all came in the opening 18 minutes and were all scored, while none of the following four were converted.