Bayern made their first step to overcoming their loss to the Nerazzurri in the May 22 final by netting a late winner through Mario Gomez to go into the return leg at home with the vital advantage of an away goal.
Inter were uncharacteristic in front of goal, with Esteban Cambiasso and Samuel Eto'o missing chances, in a contest that ebbed and flowed until the visitors hit the front in the last minute of regular time when Gomez followed up Arjen Robben's shot and knocked it from close range.
It was the German international's seventh goal of the competition, joining Chelsea's Nicolas Anelka and Eto'o at the top of the leader board.
Louis van Gaal's men will be favoured to go through when they two sides meet on March 15 at Allianz Arena with the reigning champions now in a perilous position.
Subs - Luca Castellazzi (gk), Houssine Kharja (73')
Bayern Thomas Kraft (gk), Holger Badstuber, Anatoliy Tymoschuk, Danijel Pranjic (Breno 38'), Philipp Lahm, Bastian Schweinsteiger, Luis Gustavo Dias, Mario Gomez, Thomas Mueller, Franck Ribery, Arjen Robben
Subs - Hans-Jorg Butt (gk), Breno (38')