We would then be going to Barcelona to try to win the game.
Tottenham was in danger of heading out of the competition after just four games when they went behind after 61 seconds at Wembley Stadium.
The team came out of Saturday with a 1-0 win over Vitesse, but PSV will need a similar outcome on Tuesday if it wants to avoid elimination from the Champions League.
The Dutch team had defended stoutly after Luuk De Jong's opening goal, a header from a corner, but was finally breached when Kane met a lay-off from substitute Fernando Llorente with a left-footed shot into the corner.
'We never gave up.
Although on a more positive note, Dele Alli is likely to have a place on the bench after shaking off an injury and committing his long-term future to Tottenham.
"We had to dig deep and find another level when it mattered", Kane said. We did everything, everybody was fighting for the result.
Barcelona have already secured their way out Group B after drawing 1-1 at Inter Milan last night, meaning it will come down to either the Serie A giants or Spurs to go through too.
"If we can play with that intensity, move the ball quickly, we'll get some chances and hopefully, we'll take some".
Tottenham have won eight of 11 games in the Premier League to sit fourth in the table.
PSV, which stayed on one point and can not now qualify for the knockout stage, had defended stoutly after going ahead through Luuk De Jong's header from Gaston Pereiro's corner. 'The early goal increased the belief for the opponents and we created chances and dominated the game and could not score.
For the rest of the first half the home side were dominant, but Zoet in PSV's goal was in fine form, making a brilliant double save to deny Christian Eriksen and Alli in the 28th minute.
But England captain Kane came to the rescue with a predatory equaliser before heading the crucial last-gasp victor.
Speaking about his team's performance, he added: "I think that they fight like lions".
"But I have nothing to say about the fans, I am so happy, so grateful and I understand their reaction, maybe if it was me in the stand I should be the same, but I am so happy".