Rafinha, meanwhile, was an unused substitute in the match, allowing him the time to enjoy a laugh at the expense of team-mate Arjen Robben. Robben unleashed a trademark curling effort that cannoned off the angle of post and crossbar and Lewandowski's diving header on the follow-up was brilliantly saved by the home keeper.
With more touches and passes than anyone else on the pitch, Thiago was once again sensational for Bayern and proved to be the key to unlocking the Gladbach defence with an excellent assist for Müller's goal.
It was the Germany forward's 93rd Bundesliga goal for Bayern in his 250th appearance in Germany's top flight, but only his second in the Bundesliga this season.
"I was never happy when I got substituted either when I still played", Ancelotti stressed. "We wanted to win the game", said Mueller, whose side is unbeaten in 19 matches across all competitions.
Bayern's defense held firm as midtable 'Gladbach pushed hard for an equalizer. "It was a nice day for me of course today".
"I did not expect that after their Europa League game on Thursday". It was a typical three points for the (probable) soon-to-be champs, but there was an extremely atypical moment in this one that caught the eye.
While both sides had their fair share of chances in the first half, the better opportunities went to Bayern.
Schalke 04 climbed two places to ninth as masked Bosnia defender Sead Kolasinac produced a superb individual goal after 50 minutes in their 1-0 win at Mainz.