Having beaten Hoffenheim 7-1 in the Bundesliga one week ago and FC Basel 7-0 in the Champions League on Tuesday, Bayern raced into a 3-0 lead after 19 minutes at Hertha Berlin on an evening when three of their goals came from penalties.
Thomas Muller, Toni Kroos and Mario Gomez, who took his tally to eight in three games, shared the other goals.
"That was a very impressive performance from the first seconds, the team has played outstanding football on a very difficult pitch," said Bayern sports director Christian Nerlinger.
"We must continue playing like this. If we can play with so much concentration and so convincingly, then we are certainly on the right path."
Bayern kept up the pressure on leaders Borussia Dortmund, who beat Werder Bremen 1-0 with an early Shinji Kagawa strike, while Hamburg SV's relegation worries increased with a 3-1 home defeat by fellow strugglers Freiburg.
The champions have 59 points from 26 games, five clear of Bayern. Borussia Monchengladbach, who snatched a 2-1 win at Bayer Leverkusen with Igor de Camargo's 88th-minute goal, are third on 51.
Cedrick Makiadi fired in the third following a well-worked free-kick in the 72nd minute before Ivo Ilicevic grabbed a consolation for Thorsten Fink's troubled side, who have taken one point from their last five matches.
One minute later, Christoph Janker lost possession to Robben as he tried to play his way out of defence. The Dutchman's shot was saved by Thomas Kraft only for Kroos to fire in the rebound.
