Bayern Munich swept to a 3-0 victory at home to Bundesliga rivals VfB Stuttgart to reach the quarter-finals of the German Cup on Wednesday.

England international Owen Hargreaves cracked in from 25 metres for the opening goal 10 minutes before the break and second-half goals from Michael Ballack and Dutch striker Roy Makaay sealed a commanding win.

Schalke 04 joined Bayern in the last eight with an easy 2-0 win away to second division Eintracht Frankfurt.

Hansa Rostock and SC Freiburg also made the quarter-finals on Wednesday but had to work a lot harder to do it.

Hansa needed an extra-time winner from Magnus Arvidsson to clinch a 3-2 victory away to second division Ahlen, while Freiburg scraped through on penalties against amateur club Paderborn in an afternoon match.

Arminia Bielefeld, Hanover 96 and Werder Bremen all won on Tuesday, along with Bayern Munich Amateurs, giving the Bavarian giants two teams in the last eight of the competition.

The place of Bayern's senior team was rarely put in doubt by a disappointing Stuttgart side.

Makaay twice went close with a long-range shot and a first-time waft over the bar before Hargreaves opened the scoring with a left-foot blast from outside the area.

Oliver Kahn's only problem in the first half was to deal with an unexpected hug from a supporter who ran on to the pitch dressed up as a dalmatian dog.

Stuttgart saw a little more of the ball at the start of the second half but still failed to worry Kahn and Ballack's header from a right-wing free-kick in the 69th minute gave Bayern breathing space.

Ballack capped an outstanding display by setting up Makaay to round goalkeeper Timo Hildebrand for the third 11 minutes from time.