Chelsea overcame the absence of manager Jose Mourinho to take a commanding lead in the Champions League quarter-finals.
They led after four minutes when Lucio deflected Joe Cole's shot, but Bayern's Bastian Schweinsteiger levelled.
Chelsea responded with Frank Lampard firing home a left-foot shot and then scoring an outstanding individual goal, swivelling to smash in a half-volley.
Didier Drogba powered home a fourth, but Michael Ballack's late penalty gave the Germans hope for the second leg.
The Blues showed strong resilience without the guidance of their inspirational leader Mourinho, who is serving a two-match ban and opted to watch the game on television.
He will have been impressed to see that, just like against Barcelona, Chelsea came flying out the blocks and took the lead in the opening minutes of the game.
A long ball from John Terry fell nicely for Damien Duff and he squared it for Cole.
Cole's effort from the edge of the box looked headed well wide until it took a large deflection off the unfortunate Lucio to wrongfoot Oliver Kahn.
Chelsea maintained the pressure on the Bayern goal and Kahn reacted well to punch the ball off the top of Eidur Gudjohnsen's head before Robert Kovac recovered brilliantly to deny the Icelandic forward another scoring chance.
Bayern gradually got a foothold in the game and enjoyed a period of sustained possession without troubling the Chelsea backline.
They got a helping hand in the 28th minute when Glen Johnson inexplicably opted to chest down a harmless-looking cross.
The young full-back slipped in attempting to control the ball and handed an opening to Ze Roberto who wasted the chance by blasting wide.
Chelsea remained a danger from set pieces and when Gudjohnsen cleverly laid the ball off from a deep corner Lampard struck a sweet left-foot shot that just curled the wrong side of the post.
The second half started off much like the first with Chelsea straight on the attack with a blistering counter-attack move that should have ended with another goal.
Drogba slipped it inside for Gudjohnsen, who played an instinctive first-time ball to a charging Duff who should have done better than fire at Kahn.
But Chelsea were made to pay for another needless free-kick just outside the box.
Ballack's effort was straight at the goal, but from the rebound Petr Cech could only parry Ze Roberto's shot and Schweinsteiger was in the right place to slot home.
Chelsea responded just like their manager would have wished and they took a stranglehold on the tie.
First Drogba flicked on for Lampard to find the bottom corner with a left-foot shot that just had enough pace and direction.
Lampard put the game, and the quarter-final tie, firmly in the Blues' hands with a world-class third goal for the Blues on 70 minutes.
Claude Makelele lofted a deep cross into the box and the England midfielder showed remarkable technique to control the ball on his chest, turn and lash a left-footed volley past Kahn.
Drogba made amends for some early misses when he smashed home from close range after Kahn had kept out Gudjohsen's shot 10 minutes from time.
But just as the Germans looked dead and buried Bayern gave themselves a glimmer of hope with a late Ballack penalty.
Dutch official Rene Temmink awarded the spot-kick in the second minute of injury-time for Ricardo Carvalho's challenge on Ballack and the German international easily beat Cech from the spot.
Chelsea: Cech, Johnson (Huth 65), Ricardo Carvalho, Terry, Gallas, Cole (Tiago 82), Lampard, Makelele, Duff, Gudjohnsen, Drogba (Forssell 89).
Subs Not Used: Cudicini, Smertin, Geremi, Nuno Morais.
Booked: Drogba, Ricardo Carvalho, Gallas, Makelele.
Goals: Lucio 5 og, Lampard 59, 70, Drogba 81.
Bayern Munich: Kahn, Sagnol, Lucio, Kovac, Lizarazu, Salihamidzic (Schweinsteiger 45), Frings, Ballack, Hargreaves, Ze Roberto (Scholl 73), Guerrero.
Subs Not Used: Rensing, Hashemian, Jeremies, Linke, Deisler.
Goals: Schweinsteiger 53, Ballack 90 pen.
Ref: Rene Temmink (Holland).