The German champions conceded twice in the opening 30 minutes of the International Champions Cup friendly, both coming from the head of lively Nerazzurri striker Eder.
Inter could not quite match the four goals scored by rivals AC Milan against the same opposition, but new boss Luciano Spalletti saw his side produce another assured performance to remain unbeaten in pre-season.
Bayern saw plenty of the ball in the opening stages of the match, creating a good chance through Franck Ribery after he cut in from the byline and tested Samir Handanovic with a well-taken shot down the middle.
Moments later the ball was in the net at the other end of the field, though, as Antonio Candreva's cross was allowed to bounce inside the box and Eder was there to punish Felix Gotze - younger brother of Mario - with a smart header into the top corner.
The Bavarians were struggling to create too many clear-cut openings in the first half, instead being restricted to a weak Rafinha effort on target from range and a missed back-post header from Kingsley Coman.
Inter had no such trouble getting in behind their opponents, however, with Eder again timing his run to perfection half an hour in to this time convert with his head from an Ivan Perisic cross on the left.
Eder should have been in for a third before the half-time interval, only for the officials to wrongly adjudge that he was offside, while Bayern's misery was further compounded when Ribery - the star man of their tour - hobbled down the tunnel with an injury.
Summer signing Corentin Tolisso twice failed to keep his shot on target as Carlo Ancelotti's men searched for a route back into the friendly, though Inter were also looking lively when attacking, particularly when Manchester United-linked winger Perisic got on the ball.
Both teams showed plenty of attacking intent but chances proved to be hard to come by, with Candreva and Renato Sanches relying on long-range attempts to add a third goal of the match, neither of whom succeeded.
There was a scare for Inter centre-back Miranda late on as he nearly turned the ball into his own net, if not for the intervention of Handanovic to produce a fine reaction save.
The Nerazzurri, who are back in action in less than 48 hours' time with a friendly against Chelsea here, were then able to comfortably see through the remaining 10 minutes to build up some further momentum.