Bayern Munich's Mario Mandzukic (2nd R) celebrates his second goal against Greuther Fuerth with team mates during their German Bundesliga first division soccer match in Munich January 19, 2013 (Photo: Reuters)
The hosts, who secured a major coup in midweek when they announced the signing of former Barcelona coach Pep Guardiola for next season, never hit top form in a largely one-sided game.
It was enough, however, to lift them to 45 points, with second-placed Bayer Leverkusen on 36 after beating Eintracht Frankfurt 3-1 in a game briefly delayed due to fans lighting flares and fireworks.
Croatia striker Mandzukic put Bayern into the lead in the 26th minute with a tame effort that slipped through Fuerth keeper Wolfgang Hesl's hands.
Mandzukic grabbed his 11th goal of the season on the hour when he got in front of his marker to head in a Toni Kroos corner.
Champions Borussia Dortmund, third on 30 points, travel to Werder Bremen later on Saturday.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO Sports and on Facebook at AhramOnlineSports)