Spurs’ faltering Group B campaign looked like hitting a new low after Luuk de Jong put the Dutch side ahead after only a minute at Wembley, which left Mauricio Pochettino’s men on the brink of being knocked out.
But Kane stood up when it mattered to rescue his side, equalising in the 78th minute and then being the beneficiary of an extremely kind deflection 11 minutes later to complete the turnaround.
The win, Spurs’ first of the group stage, leaves them in third place, three points behind Inter Milan, who visit Wembley in three weeks.
They will need to win that game and will have to be more clinical than they were against PSV, who should have been put to bed long before Kane’s late heroics.
Liverpool manager Jurgen Klopp thinks his side need to rediscover their mojo after a third successive away Champions League defeat left their qualification hopes in the balance.
A win in Belgrade would have left the Reds, Group C leaders going into the game, needing to avoid defeat in their final two matches to qualify but they lost 2-0 against Red Star Belgrade to leave things wide open.
Klopp admits, after failing to score here and in Naples previously, he needs to take a closer look at what has changed.
“I saw a few games like this already and it is really difficult to find your mojo back,” said Klopp.
“You don’t find solutions on the pitch, you solve problems. We made life a bit too easy tonight.
“I don’t say it is already serious if you lose twice but we have to make sure it will not not happen again.”