The Portuguese forward fired home beyond Fraser Forster to make it 4-3 just 99 seconds after Richarlison equalised for the visitors at Anfield.
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Liverpool had raced into a 3-0 lead inside the opening 15 minutes as the Merseyside outfit threatened to run riot.
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But Spurs stunned the Reds to level up the game at 3-3 in second half stoppage time courtesy of Richarlison's first Premier League goal for Tottenham.
Silence from the home supporters soon turned to delirium as Jota capitalised on Lucas Moura's short back pass to lash home into the bottom right corner.
As soon as Jota wheeled away in delight, Klopp ran to celebrate in the face of the fourth official, where he suffered an apparent injury in the process.
Klopp and the official had been at loggerheads on the touchline for the majority of the second half.
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He instantly held the back of his left hamstring, where he then hobbled off back to his dugout.
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Joking about the incident on Sky Sports, Gary Neville said: "Jurgen Klopp is laughing but he's got a grade-two tear in his hamstring!
"Liverpool were absolutely terrible in the second half but they've won the game. The emotion in this ground is unbelievable."
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Speaking of his injury to BBC Match of the Day, Klopp remarked: "I'm not sure if it's the hamstring it could be the adductor but I got punished.
"Little sins immediately. I turned around for the celebration because the fourth official got nothing wrong the whole time.
"I didn't say anything bad, I gave a look which is bad enough.
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"The hamstring or whatever the muscle gave up in that moment. That's fair. Apart from that, all okay."
The enthralling victory over Spurs has seen Liverpool leapfrog Ryan Mason's side in the table, where they sit in fifth spot.
It keeps their faint hopes of securing Champions League football for next season alive after racking up a fourth consecutive win.