This result, combined with Chelsea's failure to beat Huddersfield Town at Stamford Bridge this evening, sealed Champions League football for Spurs at their new stadium next season, and lifted them above Liverpool into third heading into Sunday's final round of fixtures.
Newcastle gave as good as they got on their first trip to the home of football in 18 years, but a splendid Harry Kane goal early in the second half was enough for Spurs.
There may have been some nerves in the home camp following Saturday's defeat to West Bromwich Albion, which saw their cushion on Chelsea cut to two points, and that showed in their first-half performance.
It was the visitors, who were on the back of three straight defeats, that created much the better chances before the break, starting with an 11th-minute Ayoze Perez shot which was saved by Hugo Lloris, after the Spaniard had easily outmuscled the much bigger Jan Vertonghen.
Lloris was beaten three minutes later when Jonjo Shelvey whipped a 20-yard free kick around the wall but back off the post, on a night when the Magpies could have easily taken a point with a slice of luck.
England World Cup hopeful Shelvey was the source of most of Newcastle's chances, teeing up Jamaal Lascelles for a header which Lloris had to push away at full stretch.
The only clear-cut opportunity that they engineered in the first half came from a long punt from Lloris, which bounced kindly into the path of Kane who fluffed his lines when one-on-one with Martin Dubravka.
Kane showed more composure five minutes after the restart to ease the tension around Wembley, cushioning a classy finish into the top corner from Son Heung-min's layoff, for his 28th league goal this term.
Newcastle continued to pose an attacking threat after falling behind as Kenedy shot narrowly wide from 25 yards out, and Lloris reacted quickly off his line to prevent Matt Ritchie from having a close-range tap-in.
Far from their fluid best, Spurs only had a couple of chances to make these precious points more secure as Dubravka saved low from Dele Alli, and again when substitute Danny Rose countered in stoppage time.
Newcastle's best chance to equalise came through a substitute of their own as Jacob Murphy skilfully rounded Sanchez, only to lose his cool when pulling the trigger, blazing a shot over from a tight angle.
The Magpies remain 10th but could finish as low as 14th with a fifth straight defeat on Sunday, when Spurs host Leicester in their final game at Wembley, relieved of the pressure of any significant final-day drama.
SPURS (4-2-3-1): Lloris; Trippier (Alderweireld, 83'), Sanchez, Vertonghen, Davies; Wanyama (Rose, 88'), Sissoko; Eriksen, Dele, Son (Lamela, 77'); Kane
NEWCASTLE (4-4-2): Dubravka; Yedlin, Lascelles, Lejeune, Dummett; Ritchie, Shelvey, Diame, Kenedy (Murphy 71'); Perez, Gayle (Joselu, 76')