The teams meet again next week at Zurich's Letzigrund Stadium and the Germans take a commanding lead into the second-leg thanks to goals from Bastian Schweinsteiger and Arjen Robben.
The hosts scored an early goal through midfielder Schweinsteiger, then doubled the lead when Dutch winger Robben curled his shot home on 72 minutes.
"In the second half we played well, we created several clear goal chances and dominated our opponents," said Bayern CEO Karl-Heinz Rummenigge. "In the first-half, we didn't really do enough, but a 2-0 result gives us a good chance of qualifying. We have to concentrate now for the second leg in Zurich and we could do with scoring a goal or two there."
But Bayern coach Jupp Heynckes was left ruing several missed opportunities,
especially in the second-half when the hosts squandered four clear chances.
"The players knew how important this game was for us," said Heynckes. "We started well in the first 20 minutes and created some good chances, but if you are as superior in the second-half as we were, we have to take our chances. We have to raise our tempo against a team like that."
And despite creating the first goal and scoring the second, Robben says there is plenty of room for improvement ahead of the second leg.
"The result is ok, but we have to concentrate more, be more aggressive and play faster," said the Dutchman.
Bayern host the Champions League final here at their Allianz Arena stadium on Saturday May 19 next year and this was the first step on what they hope will be a run to their first European title since 2001.
Heynckes sent out a strong side with each player enjoying some degree of international experience.
Germany midfielder Thomas Müller was the only star left on the bench as he opted for seven full German caps in the team, plus he started with dynamic Robben and Franck Ribery on either flank.
The selection paid off when Robben beat Zurich defender Mathieu Beda down the left flank and fired in a cross which vice-captain Schweinsteiger met at the far post after just eight minutes.
A well-struck cross from right-wing Ricardo Rodriguez, headed wide by Tunisia striker Amine Chermiti, was Zurich's best effort of the first-half - goalkeeper Manuel Neuer had it covered, but referee Aleksei Nikolaev ruled it offside anyway.
Germany striker Mario Gomez wasted a golden chance when Ribery darted into the penalty area and squared for his Munich team-mate, but Gomez fired wide with the goal at his mercy on 50 minutes.
Likewise, captain Philipp Lahm went one-on-one with Zurich goalkeeper Johnny Leoni just moments later, but his shot was saved.
Then Ribery clattered the right-hand post with Leoni beaten from a free-kick, but Robben eased Bayern's nerves with his sweetly-struck shot from the edge of the area with just under 20 minutes left.
Gomez went close again with ten minutes remaining left as he fired over as Bayern dominated until the final whistle and Zurich were reduced to ten men when Beda was sent off for a second yellow card in added time.