Inter dreaming of treble glory after reaching Champions League semis
Italian champions Inter will face Barcelona in the semis after goals in the space of three minutes from captain Lautaro Martinez and Benjamin Pavard cancelled out a Harry Kane strike for Bayern which levelled the tie in the 52nd minute.
Eric Dier's looping header in the 76th minute earned Bayern a draw on the night in soaking and blustery Milan but that wasn't enough for Vincent Kompany's side to continue their bid to be crowned kings of Europe for a seventh time.
Simone Inzaghi's side came through in awful conditions at the San Siro where a combination of heavy rain and driving winds affected both teams' ability to play their best football, but added uncertainty and tension to an already highly-charged occasion.
"We don't give up, we have personality and heart and intelligence. We were definitely on the back foot at times today but we showed again today that we can do great things," Martinez told Amazon Prime.
Inter are still on for a repeat of the Serie A, Champions League and Italian Cup treble won under Jose Mourinho in 2010, as they are also three points ahead of Napoli in Italy's top flight and face AC Milan in the semi-finals of the domestic cup.
Wednesday's win showed that Inter are more than capable of reaching the final of Europe's elite club competition, as they did two years ago when they were narrowly beaten by Manchester City.
"We think about winning everything at the start of every season, because if we don't then we shouldn't play this sport. That's our mentality," added Martinez.
Bayern had won all three of their previous Champions League away matches at Inter, but after Pavard crashed home his first goal for the club in the 61st minute there was no way back for the injury-hit Bundesliga leaders, whose the chance to win the Champions League in Munich slipped through their grasp.
"When you look at how the two games went, we wouldn't have wished for a lot different, except the goals we conceded," said Kompany.
"That's football, that's life."
Treble dream
Inter will also benefit from playing the second leg of their showdown with Barca, whom they beat in the semi-finals on their way to victory in Madrid 15 years ago, at the San Siro on May 6.
The hosts didn't come alive until their fans, who had been sat and stood in silence for the first 20 minutes in protest at ticket prices, burst loudly into song.
By that time the wind had picked up so much that one Inter cross almost swung back out of the penalty box, but even with the wind in their faces the hosts were on the up.
Marcus Thuram just failed to get a touch on Francesco Acerbi's scuffed finish in the 29th minute, and moments later Hakan Calhanoglu crashed a powerful shot just wide of the upright.
Bayern reacted and pushed Inter back into their own area for the final minutes of the opening half, but a combination of the conditions, desperate defending and poor finishing kept the match scoreless at the break.
Inter started the second half the stronger but Kane levelled the tie with a brilliantly taken goal, shifting onto his right and drilling a low angled shot through Federico Dimarco's legs and past Yann Sommer.
Just moments before Kane had rookie Bayern goalkeeper Jonas Urbig to thank for stopping him scoring an own goal, and in the 58th minute Martinez re-established Inter's advantage when he controlled Dimarco's corner and lashed home.
Pavard decided the tie three minutes later with a bullet header against his former club from another corner, sending the San Siro wild with delight.
That wasn't it though as Dier moved Bayern back to within a goal of extra time, but when Sommer smothered Kane's weak header in stoppage time Inter were still on course for the treble.