DFB-Pokal: Leverkusen 0 Bayern 0 (pens 3-5)
Pep Guardiola's side were forced to do things the hard way on Wednesday, but they held their nerve in a shootout to extend their unbeaten run in the tournament to 16 games, as Thiago Alcantara slotted home the decisive spot-kick.
Leverkusen enjoyed the better of a tepid first half, though Thomas Muller twice went close to opening the scoring for the visitors.
That sluggish first period also proved costly for Guardiola on the injury front, with centre-back Mehdi Benatia adding to Bayern's already lengthy list of fitness concerns when he was forced off with a knock.
The game stepped up a gear after the interval, with Robert Lewandowski having a goal incorrectly disallowed, while both Steffan Kiessling and Mario Gotze squandered golden chances as the game headed into extra time.
Leverkusen goalkeeper Bernd Leno was in spectacular form throughout to deny the holders on several occasions, pulling off a string of superb saves to send the match to a shoot-out, but he could do nothing to deny Bayern a place in the last four, as they kept their defence of the trophy on course.
Missing several key players through injury, Guardiola made just one change to the Bayern line up that triumphed over Borussia Dortmund last time out, with Gotze replacing the stricken Bastian Schweinsteiger.
Schmidt's Leverkusen are the form team in the Bundesliga, and they would have been ahead 15 minutes in had Kiessling – who netted twice in the 4-0 win against Hamburg at the weekend – managed to keep his header down after latching onto Roberto Hilbert's cross.
They were almost made to pay for that miss eight minutes later - Rafinha's corner falling to Muller at the back post, but his effort was blocked on the line by Wendell.
Matters were made worse for the visitors when their dreadful run of luck continued just past the half-hour mark as Benatia trudged off, with Sebastian Rode coming on in his place.
In spite of their lacklustre first-half display, it was Bayern who went closest to taking the lead when Juan Bernat found Muller in the box, but Leno rushed out quickly to smother the forward's low shot.
Lewandowski thought he had given Bayern the lead at the start of the second half when he headed in from Philipp Lahm's corner – but the referee ruled it out for a push on Emir Spahic, although contact appeared minimal.
Manuel Neuer was on top form to deny Karim Bellarabi edging Leverkusen ahead soon afterwards parrying the winger's effort away following an excellent move.
Not to be outdone, Leno matched Neuer's feat a minute later – somehow turning a venomous Lewandowski strike over the crossbar.
Leverkusen – who lifted this trophy for the only time in their history in 1993 – should have snatched victory in the dying moments of normal-time, but Kiessling failed to tap home from Bellarabi's low cross.
Extra-time began in a similar fashion, but this time it was Bayern who passed up a golden opportunity to go in front – Gotze volleying into the side-netting from the corner of the six-yard box.
The visitors dominated the extra period but Leno remained unbeaten in Leverkusen's goal – punching away Bernat's thunderous drive before parrying away another Gotze effort.
But it was the 17-time winners who kept their cool in the shootout, as substitute Thiago Alcantara ensured they joined Dortmund, Wolfsburg and minnows Arminia Bielefeld in the semi-finals.
Earlier in the day, third-tier Arminia recorded an historic win over Bundesliga high-flyers Borussia Monchengladbach, also on penalties, to seal their place in the last four.
Manuel Junglas gave the hosts the lead midway through the first half before Monchengladbach levelled within four minutes thanks to Max Kruse's spot-kick.
But, having withstood increased pressure from the visitors during the second half and into extra time, it was Arminia who held their nerve from the spot to progress to the semi-finals 5-4 on penalties.