Ange Postecoglou's side shattered Liverpool's unbeaten start to the Premier League season and extended their own thanks to the gripping climax to a pulsating clash in north London.
Jones was dismissed in the first half before Tottenham took the lead through Son Heung-min's opener.
Cody Gakpo equalised just before half-time but Liverpool were reduced to nine when Jota saw red after the interval.
It seemed Liverpool would hold out against the odds until Matip accidently diverted Pedro Porro's cross into his own net with just seconds left.
After a dismal run of one win in their previous 23 meetings with Liverpool in all competitions, Tottenham could finally savour a rare success against the Anfield outfit.
It was Tottenham's first win against Liverpool since 2017 when the north Londoners were using Wembley as their temporary home.
Postecoglou's men moved above Liverpool into second place, just one point behind Manchester City after the champions' surprise loss at Wolves earlier on Saturday.
Liverpool, beaten for the first time in nine games in all competitions, are one point behind Tottenham in fourth place.
For Postecoglou, it was an especially sweet success after he grew up in Australia idolising legendary Liverpool boss Bill Shankly as a childhood fan of the Reds' great 1970s teams.
The former Celtic boss has done a remarkable job reviving Tottenham following their woeful campaign under his predecessor Antonio Conte.
While it is too early to label Tottenham as title contenders, they have already beaten Liverpool and Manchester United, as well as drawing with Arsenal, to underline Postecoglou's impressive impact.
Postecoglou's latest memorable result was kick-started in the 26th minute when Jones' raised boot caught Yves Bissouma on the ankle.
Referee Simon Hooper initially gave a yellow card but after being told to consult the pitchside monitor he upgraded the punishment to a red.
Spurs late show
Postecoglou's men had a narrow escape when Luis Diaz sprinted onto Mohamed Salah's pass and fired into the far corner, only to see an offside flag disallow the goal.
Tottenham made the most of that escape to take the lead in the 36th minute.
James Maddison's sublime pass picked out Richarlison's run down the left flank and the Brazilian's cross was perfectly weighted for Son to flick home from close-range.
It was Son's sixth goal this season after his brace in last weekend's draw at Arsenal.
Having scored in the midweek League Cup win against Leicester, Gakpo was preferred up front to Darwin Nunez, who netted against West Ham last Sunday but had to settle for a place on the bench
Gakpo repaid Jurgen Klopp's faith in first half stoppage-time as Dominik Szoboszlai's cross was headed back across goal by Virgil van Dijk and the Dutch striker took a touch before firing a powerful shot past Guglielmo Vicario from 10 yards.
Diaz stretched to poke Salah's cross just wide from a good position as Liverpool threatened to complete their fightback.
However, Tottenham regained control after the break and Maddison's curler forced a superb save from Alisson, who made an equally good stop to deny Son from close-range.
Having injured himself while scoring Liverpool's equaliser, Gakpo was replaced by Jota at half-time.
But Jota was needlessly dismissed after 69 minutes for a sliding challenge on Destiny Udogie just 90 seconds after the Portugal forward was booked for clipping the same player.
Liverpool have already had four players sent off this season after only one Reds star was dismissed in the whole of last term.
Tottenham kept pushing in the face of Liverpool's massed defence and finally got their reward six minutes into stoppage-time.
Porro's low cross forced Matip to block but his out-stretched leg flicked the ball past Alisson to spark wild Tottenham celebrations.
