However, the two away goals could prove crucial in next week's return leg in Germany, particularly the last-minute penalty converted by Bayern's man-of-the-match Michael Ballack.
Chelsea took the lead after just four minutes when Joe Cole's right-foot shot took two deflections and left Oliver Kahn completely wrong-footed. The ball's final touch was off Chelsea striker Didier Drogba, who was clearly offside.
In a finely balanced first half the physically powerful Germans threatened to win the midfield war, but Frank Lampard and, particularly, Claude Makelele battled back to assert their authority.
No nonsense Dutch referee Rene Temmink - all 6 feet 6 inches and 17 stones of him - was a pivotal figure, angering both sets of fans with his uncompromising display.
Jose Mourinho may not have been physically present thanks to UEFA's touchline ban, but the home crowd gave him endless name-checks.
After substitute Bastian Schweinsteiger had levelled for Bayern with a powerful volley in the 52nd minute, Chelsea retook the lead thanks to a stunning Lampard shot on the hour.
Ten minutes later another Lampard volley made it 3-1 before Drogba added a fourth goal with nine minutes remaining with a close-range shot.
But Bayern's controversial stoppage-time penalty score gives the Germans a precious lifeline for the return leg.