By Mark Buckingham
Last Updated: 01/01/70 1:00am
With Werder not playing on Saturday, Bayern closed the gap at the top of the table to six points but were aided by Stefan Malz's dismissal on 24 minutes for two bookable offences.
Roy Makaay broke the deadlock two minutes after the break and the success was wrapped up by Roque Santa Cruz 14 minutes from time.
Stuttgart enjoyed an emphatic 5-1 triumph at Wolfsburg to remain on course for the third UEFA Champions League berth.
Heiko Gerber and Marco Streller put the visitors in command before Martin Petrov brought Wolfsburg back into the clash.
Philipp Lahm restored the two-goal cushion before half time and goals in the final 15 minutes from Kevin Kuranyi and Imre Szabics compounded Wolfsburg's misery.
Schalke were also in free-scoring mood as they crushed fellow European hopefuls Hamburg 4-1 on home soil.
Tomasz Waldoch and Ebbe Sand had the hosts ahead inside the half hour before Mehdi Mahdavikia's penalty breathed fresh life into the match.
Fabian Lamotte had Schalke back firmly in control before half time and Michael Delura's 55th minute strike concluded the scoring.
Bayer Leverkusen's challenge for a Uefa Cup spot stuttered slightly as they were held to a 0-0 draw at Borussia Monchengladbach.
Hansa Rostock came from behind to earn a point at Hertha Berlin with Thomas Schultz cancelling out Roberto Pinto's 59th minute opener for the hosts.
Bottom club Cologne rekindled their flickering hopes of survival with a 2-0 home success over fellow relegation battlers Eintracht Frankfurt.
Ingo Hertzsch's own goal after just five minutes put Cologne on the road to victory with the three points sealed by Lukas Podolski's 35th minute goal.
Hannover lifted themselves out of the drop zone with a strong second half performance sufficient to earn the points at 1860 Munich.
Dariusz Zuraw netted the opening goal on 71 minutes and three minutes later Thomas Brdaric eased Hannover's nerves with a clinching second goal.