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.
Kagawa scored his ninth goal of the season as Dortmund, who also hit the woodwork twice in the first half, extended their unbeaten Bundesliga run to a club record 20 games.
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.
EVER-PRESENT HAMBURG
Six-times champions Hamburg, the only ever-present team since the Bundesliga was founded in 1963, remain 14th with 27 points but are now only two clear of Freiburg, who are 16th in the relegation play-off spot.
Poor Hamburg defending allowed Johannes Flum and Daniel Caligiuri to put Freiburg 2-0 ahead by half-time.
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.
Bayern winger Franck Ribery, who tormented Hertha all match, began by bursting down the left and pulling the ball back for Muller to score from close range in the ninth minute.
Muller turned provider to set up the second for Robben three minutes later and the Dutchman was on target again in the 19th minute, converting a penalty awarded for a foul on Muller.
Kroos cleared an Adrian Ramos header off the line as Hertha tried to claw their way back into the game but two goals in as many minutes after half-time killed off the contest.
Ribery went down after Adrian Morales appeared to touch his shoulder and Gomez scored the penalty in the 50th minute for his 22nd league goal of the season.
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.
Robben completed his hat-trick by converting another soft penalty, awarded for an innocuous challenge by Ramos on Ribery.
