The margin of victory for Jurgen Klinsmann's team makes it the biggest-ever win in the first leg of the knockout stages.
Franck Ribery inspired the emphatic performance; scoring two goals and assisting in two others. Bayern are hoping to add a fifth Champions League title to their collection, a decade on from their unforgettable defeat to United in the 1999 final.
Elsewhere, Liverpool turned in a typically resilient performance to earn a 1-0 win against Real Madrid in Spain. Yossi Benayoun scored the only goal of the game with a header late in the second half.
Guus Hiddink’s first home game in charge at Chelsea saw the Blues grind out a 1-0 win over Juventus. Didier Drogba scored the only goal of the game after he latched onto Salomon Kalou’s pass.
The Italians improved after the break and Chelsea were forced to work hard for the win.
Meanwhile Villarreal preserved their unbeaten home record in the Champions League, but surrendered a potentially decisive away goal against Panathinaikos. Former Red Giuseppe Rossi scored Villareal’s goal with a penalty, but the game ended 1-1.