Champions Borussia Dortmund demolished hosts Werder Bremen 5-0 with a dazzling display of attacking football to prove they are still in the title hunt, albeit 12 points off the pace in third place.
Bayern, 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 to lift them to 45 points, with second-placed Bayer Leverkusen on 36 after beating Eintracht Frankfurt 3-1 in a game briefly halted after Frankfurt fans lit flares in the stands and ignited fireworks that went off above the pitch.
"We are satisfied with the win and another clean sheet but my team knows they did not play that well," said 67-year-old Bayern coach Jupp Heynckes, who has hinted he may continue his career after leaving Bayern at the end of the season.
"Our game was a bit rough and not as fluid as usual and Fuerth played really well, closed down most of the spaces. The first game is always a bit tricky. We saw again today that the Bundesliga is no walk in the park," he told reporters.
Fellow Champions League competitors Dortmund kicked off the year with bang and a much more convincing victory, taking Bremen apart and scoring seemingly at will with five different players on the scoresheet.
Marco Reus gave the visitors the lead by curling a superb free kick over the wall and fellow Germany international Mario Goetze added another with a deflected shot in the 19th minute.
Defender Felipe Santana, donning a face mask due to a broken nose, headed their third goal three minutes after the restart to quickly dash any Bremen hopes of a comeback in the second half.
With nine minutes remaining Robert Lewandowski was left unmarked at the far post to tap in before Jakub Blaszczykowski added another in the 85th, again from close range.
Croatia striker Mandzukic put Bayern ahead in the 26th minute with a tame effort that slipped through Fuerth keeper Wolfgang Hesl's hands after he had denied the forward with a superb save a minute earlier.
Mandzukic, expected to battle with Mario Gomez for a starting spot, grabbed his 11th of the season on the hour when he got in front of his marker to head in a Toni Kroos corner.
Leverkusen scored twice in two minutes with goals from Sebastian Boenisch and Bundesliga top scorer Stefan Kiessling, who netted his 13th of the season.
Andre Schuerrle sealed victory before Frankfurt's Alexander Meier notched his 12th league goal to reduce the deficit.
Brazilian Diego set up one goal and scored the other as Wolfsburg moved up to 13th on 22 points after a 2-0 home victory over VfB Stuttgart on coach Dieter Hecking's debut.
Mainz 05 drew 0-0 with visiting regional rivals Freiburg while Hoffenheim and Borussia Moenchengladbach also shared the points in their goalless draw.