With coach Pep Guardiola's move to Manchester City next season still making headlines, the Bavarians looked off the pace in the first half for the second consecutive game following their goalless draw against Bayer Leverkusen in the league on Saturday.
The second division club had the better chances in the first half, twice going close to scoring through striker Simon Terodde.
The Bundesliga leaders, who take on Juventus in the Champions League round of 16 later this month, had to wait 40 minutes for their first chance, with Poland striker Lewandowski firing home after a quick one-two with Thomas Mueller on the edge of the box.
The Bavarians could have scored again two minutes later when Jan Simunek was sent off for bringing down Arjen Robben in the box, but Mueller's penalty was saved by Manuel Riemann.
Bayern had it easier in the second half with Mueller delivering a cutback for Thiago Alcantara to score his first goal of the season. Lewandowski grabbed his second goal in stoppage time.
Hertha Berlin joined Bayern in the last four after seeing off second-tier Heidenheim 3-2.
On Tuesday, Borussia Dortmund booked their semi-final spot with a 3-1 win over VfB Stuttgart, along with Werder Bremen, who beat Bayer Leverkusen by the same score.
(Reporting by Karolos Grohmann; editing by Toby Davis)
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