Arsenal's controversial 1-0 victory at 18th-placed West Ham United on Sunday provided a pre-match boost for both clubs and Spurs were set to go four points clear of the drop zone when Tel produced a wonderful 50th-minute opener on Monday (Tuesday AEST).
It was followed by a moment of madness from the young forward after he caught Leeds captain Ethan Ampadu in the face with an overhead kick clearance after 69 minutes.
"He made a mistake ... but I am proud and I am happy for the mentality we show," Tottenham boss Roberto De Zerbi insisted.
"A big hug and a big kiss. Nothing more because he is a young player, he is a big talent and he score a great goal."
Dominic Calvert-Lewin emphatically converted the spot kick to set up a grandstand finish where De Zerbi turned to James Maddison, who made his first competitive appearance in 12 months after a serious knee injury.
There would be no winning goal, though, at London Stadium after Spurs goalkeeper Antonin Kinsky thwarted Sean Longstaff's powerful added-time strike before a late penalty appeal for Lukas Nmecha's tackle on Maddison was turned down to leave Tottenham only two points above the bottom three.
Kinsky was called into action on 21 minutes - brilliantly keeping out Joe Rodon's header - before Tel, Richarlison, Joao Palhinha and Rodrigo Bentancur all went close for Spurs.
Leeds' Ao Tanaka sliced off target before Tottenham survived a penalty shout for Destiny Udogie's collision with Calvert-Lewin.
Spurs built on that close call and a moment of magic provided the breakthrough.
Porro's corner was cleared out to Tel, who took a touch and produced a wonderful curled finish into the top corner for his fourth goal of the campaign.
It should have been 2-0 when Randal Kolo Muani teed up Richarlison, but he blazed over.
With 21 minutes left, Daniel Farke's side received a gift.
After Spurs dealt with the initial ball into the area, Tel's attempted acrobatic clearance caught the face of Ampadu and Australian referee Jarred Gillett awarded a penalty after a lengthy VAR check and pitchside monitor review.
Calvert-Lewin drilled into the bottom corner for his 14th goal of an excellent season to bring Tottenham right back into a survival battle.
"It will be tough until the last minute against Everton, for sure but ... we can't forget after four games in a row we made eight points," De Zerbi insisted.
"And West Ham they have to also play Leeds at home. I think Leeds they will play like today with the same spirit, with the same qualities."
