The English team was in danger of heading out of the competition after just four games when it went behind after just 61 seconds at Wembley Stadium.
Instead, Kane’s goals — in the 78th and 89th minutes — gave Tottenham a glimmer of hope of a top-two finish in Group B with matches still to come at home to Inter Milan and away to already-qualified Barcelona. Tottenham is in third place, three points behind second-place Inter.
“We had to dig deep and find another level when it mattered,” Kane said. “We have been grinding results out here and there all season. We are getting wins.”
In the Premier League, maybe, but this was Tottenham’s first victory in its Champions League group and there was a touch of fortune about it.
For the winning goal, Kane met a cross from Ben Davies with a header that was directed straight at goalkeeper Jeroen Zoet. The ball, however, deflected into the net off PSV defender Trent Sainsbury, who held his head in his hands.
PSV, which stayed on one point and cannot now qualify for the knockout stage, had defended stoutly after going ahead through Luuk De Jong’s header from Gaston Pereiro’s corner. It was the earliest goal Tottenham has conceded in a Champions League game.
Zoet, in particular, had a brilliant game, repelling a slew of first-half efforts from Spurs — including two in succession off Dele Alli and Christian Eriksen.
The visiting defense was finally breached when Kane met a lay-off from substitute Fernando Llorente with a left-footed shot into the corner. There was more to come from the England striker.
“This team is growing up,” Tottenham manager Mauricio Pochettino said. “The team is fighting so I am so happy.
“We have the character of never giving up which is so important.”
Inter drew 1-1 with Barcelona in the other Group B game on Tuesday, a result that saw Barca become the first team to reach the round of 16.