Having set a new UEFA Champions League record of ten consecutive victories with their 3-1 win at CSKA Moscow on Wednesday, Bayern again cruised to victory in Munich.
Even with hamstring-victim Philipp Lahm, plus France's Franck Ribery and Germany star Bastian Schweinsteiger on the walking wounded list, Bayern had too much fire-power for Braunschweig.
Having warned his side not to underestimate Eintracht, who have never won in Munich, Netherlands winger Robben was as good as his word. The Dutch star put the hosts ahead with a header after just two minutes, then slammed home a 30th-minute shot, but this was not an impressive performance as Bayern barely got out of second gear.
Borussia Dortmund picked up their first win in three league games with a hard-fought 3-1 win at ten-man Mainz to stay third and seven points behind Bayern. Dortmund took the lead on 70 minutes when Gabon's Pierre-Emerick Aubameyang fired home a superb free-kick, but the lead lasted just four minutes before Cameroon's Eric Choupo-Moting fired home a penalty.
Mainz were reduced to ten men when Colombia's Elkin Soto was sent off for stopping the ball going into the net with his hand and Poland striker Robert Lewandowski fired home the 79th-minute penalty.
Lewandowski then made sure of the points with his second penalty when he converted the 94th-minute spot kick when left-back Erik Durm was up-ended.
Bayer Leverkusen bounced back from their 5-0 drubbing at home to Manchester United in the Champions League on Wednesday - their worst home result in Europe - with a 3-0 win at home to Nuremberg to stay second.
Schalke, who have lost left-back Dennis Aogo for the rest of the season with a knee injury, moved up to fifth with a 3-0 win at home to Stuttgart.
Mid-table Werder Bremen warmed up for next Saturday's visit of Bayern with a point at Hoffenheim in an eight-goal thriller as sub Philipp Bargfrede - with the Bremen squad No44 - equalised in the 91st-minute to make it 4-4.
Augsburg - who face holders Bayern Munich on Wednesday in the third round of the German DFB Pokal - warmed up with a goalless draw in the capital against Hertha Berlin.