Bayern Munich's Thomas Mueller (25) celebrates after he scored against Paderborn during their German first division Bundesliga soccer match in Munich September 23, 2014. [Photo/Agencies]

Still missing winger Franck Ribery and playmaker Bastian Schweinsteiger among several absentees, Bayern looked sharper than in Saturday's goalless draw at Hamburg SV and should have had at least two more goals by halftime.

"I am very satisfied with our performance today," Bayern coach Pep Guardiola said. "We improved the way we play the game and we also improved our buildup."

Goetze tapped in from close range in the 78th to more accurately reflect Bayern's dominance before Mueller completed a quick move five minutes before time.

Schalke 04 bounced back from a bad start to clinch their first win of the campaign with a 3-0 victory at Werder Bremen.

The Ruhr valley club shrugged off the absences of suspended Kevin-Prince Boateng and Julian Draxler, to score twice in three minutes soon after halftime through Max Meyer and Roman Neustaedter.

Tranquillo Barnetta's 85th minute goal after good work from Klaas-Jan Huntelaar sealed the three points and offered some much-needed respite to coach Jens Keller.

Borussia Dortmund, on six points, host last-placed VfB Stuttgart while Bayer Leverkusen, a point ahead, entertain Augsburg on Wednesday.