Kane scored twice late on, however, the latter a deflected header past Jeroen Zoet, to lift his side to within three points of next opponents Inter Milan.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Gazzaniga; Aurier, Alderweireld, Sanchez, Davies; Eriksen, Dele, Winks; Lucas, Son, Kane
SUBS: Vorm, Trippier, Walker-Peters, Skipp, Sissoko, Lamela, Llorente
STARTING XI: Zoet; Dumfries, Schwaab, Viergever, Angelino; Rosario, Hendrix, Pereiro; Bergwijn, De Jong, Lozano
SUBS: Room, Sainsbury, Behich, Ramselaar, Guti, Mauro, Malen
Mauricio Pochettino: "We hope we can pay back all the effort by winning on Tuesday, it's the only way we can repay [supporters]. Of course, we all expected to be in the new stadium in this period. We cannot ask more from them. We, the club, [chairman] Daniel [Levy], we feel sorry for them. We can only be grateful - as to be at Wembley for them is tougher than it is for us."
Mark van Bommel: "It's outright disturbing. Every time I had to check whether the ball was in the sidelines. But we should not complain about it. It cannot be an excuse. Although I do not think they are happy about this in England. If you are thinking about the pitch then it is not good. You have to prepare and that is it. You cannot complain, you cannot change the situation."
TOTTENHAM HOTSPUR SUBS: Vorm, Trippier, Walker-Peters, Skipp, Sissoko, Lamela, Llorente
PSV EINDHOVEN SUBS: Room, Sainsbury, Behich, Ramselaar, Guti, Mauro, Malen