Romelu Lukaku's miss proved decisive after the shoot-out started with nine successful spot-kicks, as Bayern gained some revenge for their defeat by Chelsea in the 2012 Champions League final.
Fernando Torres had broken the deadlock in Prague with a wonderful first-time strike from Andre Schurrle's cut-back following a swift counter-attack in the eighth minute.
Bayern responded strongly and carved out a number of chances to equalise before half-time, but they had to wait until the 47th minute to draw level when Franck Ribery blasted a long-range strike past Petr Cech.
The German side continued to boss proceedings but Chelsea remained dangerous on the break and Oscar, Branislav Ivanovic and David Luiz all came close to netting a winner in normal time, before Ramires was dismissed for a second bookable offence after 85 minutes.
Eden Hazard restored Chelsea's lead early in extra time with a fine solo goal and it looked like being the winner as Cech made several great saves, until Javi Martinez struck in the dying seconds to send the Super Cup to penalties for the first time and Manuel Neuer kept out Lukaku's spot-kick.
With Jose Mourinho and Pep Guardiola renewing their tactical rivalry from their time in Spain, it was Chelsea who drew first blood on eight minutes through Torres.
Torres, restored to start following a striker-less line-up at Manchester United, firing powerfully home from Schurrle's cross in the eighth minute after Hazard had launched a fast break.
Bayern dominated after the goal, with Chelsea starved of possession and squeezed into their own half, but they had to wait until the second period to level when Ribery succeeded where he had narrowly failed in the first period.
The Frenchman cut in from the left before scoring with a fierce right-foot shot.
Neuer spread himself well to save from Oscar and Frank Lampard fired the rebound over.
Luiz antagonised Bayern at every set-piece and was booked for a foul on Mario Mandzukic in an increasingly feisty encounter.
Toni Kroos and Jerome Boateng had efforts before Ivanovic hit the crossbar with a header and Neuer held a Schurrle shot.
Ramires was sent off for a foul on Mario Gotze which earned him his second yellow card, putting Chelsea under further pressure.
Bayern tried to win the game in the remaining five minutes of normal time and Ribery fired wide after a one-two on the edge of the area with Gotze before the whistle blew and Mourinho and Chelsea players hounded the officials.
It was the 10 men of Chelsea who re-took the lead, when Hazard danced in from the left, by the static Martinez and Boateng, before drilling low into the net.
Cech saved a Xherdan Shaqiri effort as Bayern attempted to respond for a second time, but the Blues reached the extra-time interval knowing they had to survive for 15 minutes more.
Mandzukic was twice denied by Cech and Shaqiri was unable to divert a Martinez header down goalwards following a great clearance by Gary Cahill.
Mourinho threw John Terry into the action, in place of Hazard, for the final seven minutes, as Bayern continued to go forward.
Cech saved from Gotze and Ribery but could not hold out as Martinez netted with the last kick of extra-time to force penalties.And on this occasion, Bayern triumphed.
|Chelsea||Team Statistics||FC Bayern München|
|6||Shots on Target||10|
|5||Shots off Target||18|
|300||Total Passes (All)||846|