Having set a new Champions League record of ten consecutive victories with their 3-1 win at CSKA Moscow , Bayern again cruised to victory in Munich.
"It was a complicated and difficult game against a defence-minded opponent," said Bayern boss Pep Guardiola, who with 12 wins and two draws, has extended his record for the best start by a new Bundesliga coach.
"We dominated possession and, in the first half, we were very strong mentally after (last Saturday's 3-0 win at) Dortmund and the trip to Moscow.
"In the second half we didn't manage to bring (striker) Mario Mandzukic into the game, but it is one game more and at the end, I am happy with the performance."
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, Dutch winger Robben was as good as his word.
The Netherlands 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 05 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 10 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.
"You have to evaluate the win in the context of our situation," said Dortmund coach Jurgen Klopp, who lost his entire back four ten days ago through injury.
"There was a very, very good fighting spirit. The fact that in certain situations our opponents had their chances to win the game says everything about Mainz's class."
Bayer Leverkusen bounced back from their 5-0 drubbing at home to Manchester United in the Champions League — their worst home result in Europe — with a 3-0 win at home to Nuremberg to stay second.
South Korea striker Son Heung-Min netted twice while Germany's Stefan Kiessling hit their second after a superb back-heel from midfielder Jens Hegeler.
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 VfB Stuttgart.
Peru winger Jefferson Farfan scored twice, including a penalty early in the second-half, before US midfielder Jermaine Jones added a late third.
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 number 44 — equalised in the 91st-minute to make it 4-4.
Augsburg — who face holders Bayern Munich in the third round of the German Cup — warmed up with a goalless draw in the capital against Hertha Berlin.
, Hamburg continued their revival under ex-Holland boss Bert van Marwijk with a 1-1 draw at fifth-placed VfL Wolfsburg.