Having orchestrated Bayern's home win over FC Zurich in a Champions League qualifier on Wednesday, Robben ran the opposition ragged and scored as the Bavarian giants dismantled Hamburg at Munich's Allianz Arena.
"When everyone is fit we could score more goals, we were very disciplined," said Robben, who came off after 66 minutes with his side 4-0 up as he is still recovering from a back injury.
"I felt better than I did against Zurich, but the pain got worse in the second half and I thought it was better to come off. There is still more to come from me and this team."
Bayern coach Jupp Heynckes said he was happy his side kept a clean sheet for the third time in a row.
"This was our best performance of the season," he said. "I am especially pleased that we not only created an abundance of goal chances, but we stopped the opposition from scoring again."
Winless after the first three games, Hamburg captain Heiko Westermann admitted he was again perplexed with his side's performance.
"This is inexplicable," said Westermann. "We just have to produce on the pitch the things we do in training. It is high time we win at home (next week against Cologne)."
Bayern are now up to second in the table behind surprise early leaders Borussia Mönchengladbach.
First towering Belgium defender Daniel van Buyten buried his header from a Robben free-kick on 13 minutes and then French winger Franck Ribery danced around defenders to score the second.
Having already torn huge holes in the Hamburg defence, Robben made it 3-0 after 34 minutes when he beat two defenders and chipped Hamburg goalkeeper Jaroslav Drobny.
A deft back-heel from Thomas Mueller allowed Mario Gomez to fire home after 56 minutes before substitute Ivica Olic's header after 80 minutes sealed the rout.
Having suffered a shock defeat at Hoffenheim last week, champions Dortmund enjoyed a hard-fought win at home to Nuremberg.
A well-timed pass from Germany star Mario Götze on 50 minutes found Poland striker Robert Lewandowski in the heart of the penalty area and he fired home before Germany winger Kevin Grosskreutz added the second, 10 minutes from time.
"Nuremberg defended really well for long stretches and showed plenty of initiative," said Dortmund coach Jürgen Klopp.
"It was hard work for us and in the second-half we were variable. It was not a pretty win for us, but it was a deserved one."
Last season's runners-up Leverkusen had a 1-0 win at 10-man Stuttgart, who had Holland defender Khalid Boulahrouz sent off for insulting the referee with time almost up.
The visitors took the lead when midfielder Michal Kadlec fired in a shot after 28 minutes which goalkeeper Sven Ulreich could only block with Stefan Kiessling waiting to stab the ball into the net.
Werder Bremen earned a dramatic 5-3 win at home to Freiburg as Papiss Cisse scored twice for the guests, but ended on the losing team after midfielder Aaron Hunt netted an 86th-minute penalty and Wesley scored in extra time.
Newly-promoted Augsburg are still looking for their first ever Bundesliga win after they lost 2-0 at Hoffenheim, while the guests picked up their second straight win.
Suffering from a fever, Germany striker Lukas Podolski missed Cologne's 1-1 draw at home to Kaiserslautern on Saturday night which kept his side at the foot of the table.
On Friday, 'Gladbach had continued their storming start to the season as a Marco Reus double helped them to a 4-1 victory over Wolfsburg to go top spot.
After beating Bayern in the opening match of the season, Mönchengladbach came back from a goal down and are now one point ahead of unbeaten Mainz 05, who host Schalke 04 on Sunday, and Hanover, who play Hertha Berlin the same day.