Bayern Munich suffered its first Champions League home defeat in 22 matches, falling 2-1 to Inter Milan in the first leg of their quarterfinal at the Allianz Arena on Tuesday.

The hosts started brightly, with Michael Olise and Harry Kane testing Inter keeper Yann Sommer early on, while Raphael Guerreiro had the clearest chance of the half, only to be denied by the Swiss shot-stopper.

The usually reliable Kane missed a golden opportunity from close range on the half-hour mark, a moment that seemed to shift the momentum. Inter punished Bayern's wastefulness just before the break, when Lautaro Martinez finished brilliantly from the edge of the area after Marcus Thuram's backheel assist.

Bayern pushed forward in the second half but struggled to break down the best defence in the competition. Guerreiro and Josip Stanisic both went close, while Leon Goretzka made a crucial block to deny Inter a second goal at the other end. Vincent Kompany turned to his bench with 20 minutes remaining, sending on Thomas Muller, Serge Gnabry and Sacha Boey in search of a breakthrough.

The move almost paid off. Kane fired wide and was later saved by Sommer, but it was Muller who finally drew Bayern level in the 85th minute, converting Konrad Laimer's cross from close range. But their joy was short-lived. Just three minutes later, Inter caught Bayern on the break and Carlos Augusto found Davide Frattesi, who slotted the winner into an empty net.

Bayern now heads to the San Siro needing a comeback to keep its Champions League hopes alive.

"We tried to fight our way back and we managed to do that, but we definitely could've handled the final moments better," said Muller. "It's 2-1 to Milan after the first leg, not the result we had in mind, but the tie is far from over."

"We had our chances to score in the first half, we played with courage and created danger," said Bayern coach Kompany. "It's a pity we conceded that late goal, but we have the opportunity next week to make things right."