BERLIN, Dec 20 (Reuters) -- A stoppage-time goal by Dutchman Arjen Robben sent Bayern Munich into the German Cup quarter-finals with a nervous 2-1 win over second division VfL Bochum on Tuesday.

Robben struck seconds before the final whistle after Bayern came from a goal down to level early in the second half.

Bochum showed no fear against the Bundesliga leaders and deservedly grabbed the lead midway through the first half with Giovanni Federico tapping in from close range after keeper Manuel Neuer failed to reach a Mirkan Aydin low cross.

Bayern brought on Bundesliga top scorer Mario Gomez for Ivica Olic, who had started instead of the Germany international, after the break and the change paid off as the visitors charged forward.

Jerome Boateng hit the crossbar right after the restart and Franck Ribery fired narrowly wide. Toni Kroos was on target in the 52nd minute after a fine one-two with Gomez to level.

But the Bavarians had to wait until stoppage time to finally break the resistance of Bochum with Robben firing in from 10 metres after a pass from Ribery and continue their quest for a treble this season.

Fellow Bundesliga club Nuremberg slumped to a 1-0 defeat to second division club and local rivals Greuther Fuerth courtesy of a 15th-minute goal by Edgar Prib.

Champions Borussia Dortmund take on second division's Fortuna Duesseldorf later on Tuesday while holders Schalke 04 travel to Borussia Moenchengladbach on Wednesday.

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