Real, fraught with the public fight between coach Zinedine Zidane and player Gareth Bale, had been hoping for a win after a big loss to Atletico Madrid.
Spurs also needed a win after their loss against Manchester United.
Bale was not with the squad in Munich, with Zidane saying the Welshman had chosen to stay behind for medical reasons.
Tottenham coach Mauricio Pochettino said there was still room for improvement for his team but added that the win had been important.
(Production: Ayhan Uyanik, Tanya Wood)