Bayern held their nerve in front of a sell-out crowd of 69,000 at their Allianz Arena after United strikers Wayne Rooney and Michael Owen missed great chances in the second half to win the match.
Bayern enjoyed the better of the first half, in which Mario Gomez and Dimitar Berbatov both hit the woodwork, but United then had the better opportunities after the interval - only for Rooney and Owen to fail to beat Bayern goalkeeper Michael Rensing in one-on-one situations.
Rensing proved to be Bayern's hero as he made saves from Patrice Evra and Jonny Evans in the shoot-out before Daniel van Buyten stroked in the winner.
United manager Sir Alex Ferguson changed his entire starting XI from Wednesday's 2-1 win against Boca Juniors, with Owen and Berbatov leading the attack and Ryan Giggs given the captaincy.
Bayern coach Louis van Gaal also made wholesale changes with Breno and Martin Demichelis coming into the centre of his defence, Anatoliy Tymoschuk commanding the midfield and Rensing returning in goal.
The changes had not done much to slow the momentum Bayern had built up in their 4-1 win over AC Milan 24 hours earlier.
Gomez went close to breaking the deadlock in the 18th minute when he hammered a 12-yard shot on the stretch against Edwin van der Sar's crossbar.
Thomas Muller, whose double saw off Milan, missed the chance to add to his impressive tally of pre-season goals when he shot straight at Van der Sar after being released by Alexander Baumjohann in the 28th minute.
Five minutes later, Bayern were pleading for a penalty when Muller fell under the challenge of Jonny Evans, but referee Dr Felix Brych waved play on.
The Red Devils had to be patient before creating their first chance of the match five minutes before the interval.
Bayern failed to clear their lines after a Giggs corner had been flicked on to Berbatov by Rio Ferdinand and Owen only just failed to bundle the ball over the line.
The ball than sprang up for Berbatov to try an acrobatic overhead kick which cannoned off Rensing's
right-hand post with the Bayern goalkeeper beaten.
United started the second half a lot brighter with Berbatov going close with a header from a Giggs free-kick before Owen had a chance to punish Bayern for losing possession in midfield.
The lively Nani was quick to react when Hamit Altintop lost the ball on the halfway line and he passed on the responsibility to Paul Scholes, who in turn threaded a pass into the path of Owen, but he arrowed his shot straight into the chest of Rensing.
Ferguson brought Wayne Rooney, Anderson and Antonio Valencia on and the fresh legs spurred them forward for one final assault on the Bayern goal.
Rooney should perhaps have grabbed a winner five minutes from time when he was put through by Giggs, but he blazed his angled shot high and wide with just Rensing to beat.
The game had to be decided by a penalty shoot-out, and another dose of England against Germany spot-kick drama.
Rensing made a one-handed save to deny Evra, but Van der Sar responded with a save from Daniel Pranjic.
Rooney scored United's fifth penalty, putting the pressure on Jose Ernesto Sosa, who found the bottom corner to force sudden death.
Evans had his effort saved by Rensing, leaving Van Buyten to score the winning penalty.