
Tournament hosts Bayern named a youthful side for Wednesday’s game at the Allianz Arena, Niko Kovac’s side having thrashed Fenerbahce in the semi-finals a day earlier.
Spurs seemed set to follow their Real Madrid win with victory over the Bundesliga champions by going 2-0 up thanks to goals from Erik Lamela and Christian Eriksen.
But Jann-Fiete Arp pulled one back for Bayern, who equalised in style thanks to a superb long-range hit from Alphonso Davies, only for Paulo Gazzaniga to deny Boateng in the shoot-out.
Manuel Neuer brilliantly thwarted Lucas Moura in the fifth minute as the Brazilian tried to turn home an excellent right-wing cross from Kyle Walker-Peters.