Newcastle have lost five of their last six opening games to a league season, drawing the other vs Southampton in 2015-16, making it another horror start for Rafa.
A thrilling first 20 minutes saw all three of the game's goals scored.
The visitors needed just eight minutes to get their noses in front when, after Magpies goalkeeper Martin Dubravka had turned away a Christian Eriksen shot, the Denmark international delivered the resulting corner for defender Davinson Sanchez to attack.
The Colombian's header down was met at the far post by Jan Vertonghen under pressure from Paul Dummett and the ball ricocheted down from the crossbar, with referee Martin Atkinson awarding the goal after being alerted that the ball had crossed the line.
However, the lead lasted just three minutes as Joselu rewarded manager Rafael Benitez for his faith in picking him ahead of summer signings Salomon Rondon and Yoshinori Muto.
Matt Ritchie cut back on to his left foot and curled in a cross which the striker met unopposed to glance a header past Hugo Lloris.
Spurs continued to dominate possession and regained their lead with just 18 minutes played when full-back Serge Aurier drove a cross to the far post for the unmarked England international Alli - who overcame any post-World Cup rustiness - to power a header past Dubravka.
Substitute Rondon, a loan signing from West Brom this week, almost snatched a point five minutes from time when his shot hit Vertonghen and looped over Lloris, only for the ball to come back off the crossbar.
Tottenham have won four of their last five Premier League visits to St James' Park.