The Bavarians, who have now kept a clean sheet in their last seven games in all competitions having won six, took charge inside 13 minutes through Lewandowski, who controlled a superb Rafinha pass, and Robben after he pounced on a Hanover mistake.
Poland striker Lewandowski, who joined from Dortmund this season, benefited from another superb through ball in the 38th minute, this time form Juan Bernat, for his fourth league goal of the campaign.
Robben also got a second goal, slotting the ball home 11 minutes from time as undefeated Bayern moved up to 17 points with the team in a good mood as they prepare for an official Oktoberfest beer festival visit on Sunday.
"Maybe it was our best performance yet (this season)," Robben, who improved his already sparkling record to 59 goals and 42 assists in 110 Bundesliga games, told reporters.
"We had fun on the pitch and it was also great for our fans.
"We played very aggressively up front and created a lot of chances. We should have scored even more but 4-0 is good enough," said the Dutchman, who added that it was now time to celebrate with a beer at the city's Oktoberfest.
"I'll go today as well without the family and tomorrow I'll be with the family," said the winger with a wide grin.
DORTMUND CRISIS
But there was no party atmosphere in Dortmund, who lost 1-0 to relegation-threatened Hamburg as they continued a disastrous league start with their fourth defeat in seven games on the back of their dominant midweek Champions League win over Anderlecht.
Pierre-Michel Lasogga snatched the winner in the 35th minute following an Adrian Ramos mistake as last season's runners-up dropped to 13th on seven points, 10 behind Bayern after seven games. Hamburg moved off the bottom to 17th on five points.
Dortmund posed little threat for much of the game and left it late to push for the equaliser.
They failed, however, to beat Hamburg keeper Jaroslav Drobny in a frantic finale with the 34-year-old also doing well to deny Ramos from point blank-range in the 72nd.
Fellow Champions League club Schalke 04 continued their rollercoaster season, losing 2-1 at Hoffenheim, who are second on 13 points.
Bayer Leverkusen salvaged a 2-2 draw against 10-man Paderborn with a 90th-minute Karim Bellarabi equaliser to drop to fourth on 12.
Eintracht Frankfurt joined them on 12 points after Alexander Meier scored twice in an entertaining 3-2 victory over promoted Cologne.
Werder Bremen are still the only team without a win this season and remain in last place after drawing 1-1 at home to Freiburg.
(Editing by Ed Osmond and Ken Ferris)
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