It was arguably the Magpies’ best result under Eddie Howe, with this victory making it four wins in five games for the north-east club, who ultimately hold long-term aspirations of being Champions League regulars.
This statement win consigned Spurs to back-to-back defeats and occurred amid some controversy, with the hosts unhappy no foul was awarded against Wilson, who collided with Hugo Lloris in the build-up to his lobbed opener.
Almiron added a second for the visitors nine minutes later with 40 on the clock and while Harry Kane pulled one back early in the second half, Newcastle held on to leapfrog Chelsea and Manchester United in the table.
Both clubs experienced contrasting midweek results and the hosts’ hopes of bouncing back from defeat at Old Trafford was not helped by the absences of Cristian Romero and Pierre-Emile Hojbjerg due to minor injuries.
A frantic start saw Son Heung-min let fly twice in quick succession while the visitors forced two corners in the first 10 minutes, with penalty appeals on Joelinton waved away after he clashed with Emerson Royal.
Spurs should have broken the deadlock not long after when Kane sent Son through, but he hesitated and his weak chip was saved by Nick Pope from close range.
Eric Dier was the next to go close to putting through his own net after his overhit back pass to Lloris bounced yards wide of the home goal.
Antonio Conte’s team were able to shake off that scare, with Ryan Sessegnon having an effort deflected wide before Kane was denied by Pope’s left foot after a fine run.
It appeared Tottenham were edging closer to the opener when they were undone by a Lloris error in the 31st minute.
Fabian Schar sent a ball over the top for Wilson to chase and although Lloris was first to it, the Spurs goalkeeper went down under slight contact from the Newcastle forward.
Wilson carried on while Lloris was on the floor and lobbed both the France international and Dier before he wheeled away to celebrate.
A VAR check came and went which only added to the frustration of the hosts – but even worse was to follow.
Sean Longstaff headed down an attempted pass by Lloris to Almiron, who embarked on a jinking run that saw him beat Sessegnon and Clement Lenglet before he fired under the Tottenham goalkeeper for his sixth goal of the campaign.
Boos followed from the home supporters at half-time and so did rain and lightning, with the bleak weather matching the mood at Spurs.
Not that the Newcastle fans were bothered, with several topless despite the heavy downpour, but they were up in arms in the 51st minute when no penalty was given after Joelinton’s header hit Emerson’s arm.
It could have been 3-0 from the resulting corner but Lloris got down low to deny Schar and the momentum of the fixture quickly swung.
Spurs forced a set-piece of their own and Son’s delivery was flicked on by Lenglet to the back post where Kane stooped low to head in his 11th goal of the campaign.
VAR was required to see if Davinson Sanchez had got a touch but, with no conclusive evidence either way, Stockley Park-based Stuart Attwell let the goal stand.
Ivan Perisic and Lucas Moura were sent on by Conte soon after that 54th-minute effort.
Perisic sent a curler straight down Pope’s throat and Dan Burn impressively blocked a close-range Son effort as Tottenham suffered a first home defeat since April.