In an explosive first half in which Bayern were 4-0 up inside half an hour, the Poland striker, who has notched a staggering 10 goals in their last three matches, including five in nine minutes against VfL Wolfsburg in the Bundesliga, struck twice in seven minutes.
"He is having an amazing run and an unbelievable week behind him," Bayern captain Philipp Lahm told reporters. "A striker like Lewandowski doesn't need any prodding. He could be even more dangerous than last season."
Brazilian Douglas Costa had put the hosts ahead with a fine low shot after 13 minutes and Mario Goetze added his second of the campaign before Poland captain Lewandowski chipped keeper Eduardo in the 55th minute for his third goal as Bayern moved to a maximum six points from two matches.
Greek champions Olympiakos stunned Arsenal 3-2 to move into second place level on three points with Zagreb, leaving their hosts bottom without a point.
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"I want to congratulate my players for tonight," Bayern coach Pep Guardiola said. "They had a top performance. With (wingers) Douglas Costa and Kingsley Coman our game is much better. Robert and Thomas (Mueller) have much more space in the middle.
"Now we are off to the Oktoberfest and then we will start thinking about Borussia Dortmund on the weekend," he added referring to their top-of-the-table Bundesliga clash.
Dinamo, unbeaten in 45 games matches in all competitions before Tuesday and winners at Arsenal in their opening group game, were mere observers as they witnessed Bayern's awe-inspiring display of speed, skill and strength.
MUELLER BENCHED
Bayern coach Pep Guardiola surprisingly left Thomas Mueller and Xabi Alonso on the bench, playing the talented Joshua Kimmich instead.
The 20-year-old needed three minutes to make his presence felt, although his glancing header sailed narrowly over the bar.
Eduardo came to the rescue a little later, palming a powerful Jerome Boateng drive around the post but could do nothing when Costa charged into the box and caught him off guard from a tight angle.
His 13th-minute goal opened the floodgates and Bayern doubled their lead in the 21st when Thiago Alcantara pounced on a mistake by Filip Benkovic and laid the ball off for Lewandowski, who had no trouble tapping in.
Goetze was then on target after playing a clever one-two with Kingsley Coman in the 25th and Lewandowski flicked in a Costa corner three minutes later with the ball going in off the bar.
The 27-year-old Lewandowski, who also scored twice against Mainz 05 in the Bundesliga on Saturday, completed his treble 10 minutes after the restart with a fine turn and chip after a backheel combination between Costa and Thiago left the Dinamo defence dazed.
(Reporting by Karolos Grohmann; editing by Ken Ferris and Ed Osmond)
