United had more possession, but the visitors the better chances, besides Sergio's short-range goal in the 86th Alexander Zickler's blast against the crossbar, in in the teams' first meeting since the legendary 1999 final where United won 2-1 from two injury-time goals.
The three-times champions Munich are now well-positioned to complete their revenge mission in the second leg in their Olympic stadium after their first ever win against United in four meetings. They have never lost a knockout tie after winning on the road.
United, meanwhile, face elimination in the quarter-finals like last year against later champions Real Madrid after a 3-2 home loss. In addition, they also lost the last knockout home leg for the against a German team as Borussia Dortmund had won 1-0 in the semis en route to the 1997 title.
"It was important that we controlled the game. We thought they would get nervous in the end," said Munich coach Ottmar Hitzfeld, who was Dortmund's helmsman at the 1997 game.
Captain Stefan Effenberg said "this was the true Bayern Munich," but remained cautious: "We have to play fully concentrated in Munich and can't sit back."
The second meeting will take place without David Beckham because the England international has to serve a yellow-card suspension. But Munich's Hasan Salidamidzic and Bixente Lizarazu will also have to sit out the game.
Determined to get a decent cushion for the second leg meeting, United pressed from the start in front of a sellout 76,500-strong Old Trafford crowd but failed to create serious danger.
The first chance of the match belonged to Munich when Paul Scholes needed to clear Patrick Andersson's header off the goal-line in the 17th.
Seconds later David Beckham superbly fed Andy Cole on the left edge of the area, but the striker didn't get a clean volley and the ball sailed high over Oliver Kahn's goal. Cole missed again in the 24th and Ryan Giggs shot wide in the 39th.
The 19974-1976 champions Bayern tried their luck with counter attacks with Carsten Jancker aiming right at Fabien Barthez in the 22nd and Hasan Salihamidzic misfiring from a great position in the area six minutes later.
The game became more balanced after the break as Munich gave up their cautious approach and soon controlled the action.
United hardly threatened while there was plenty of danger on the other end in front of a more and more subdued crowd.
Stefan Effenberg's freekick sailed high in the 47th, Giovane Elber's blast was tipped over the bar by Barthez in the 53rd and the French international goalkeeper was also on his guard against Jens Jeremies' drive in the 65th.
The substitute Zickler almost delivered in the 82nd when he fired against the crossbar, but Munich then went on top for good when Thomas Linke headed on a deep pass and Sergio cooly slotted home from short range.
(kil/dpa)