Lewandowski was on target twice against Peter Bosz’s men, with further goals from David Alaba and Serge Gnabry consigning Leverkusen to a 4-2 defeat.
It marked the second straight season Bayern have won the league and cup double, and given they are still going strong in the UEFA Champions League, which resumes next month, the Bavarians could clinch an unprecedented treble to complete a remarkable season.
Lewandowski has taken his tally for the season to 51 goals in all competitions and he is now the outright top scorer in the Bundesliga (34), DFB-Pokal (6) and Champions League (11) this season.
Flick backed Lewandowski for Ballon d'Or glory post-match, telling reporters: "Fifty-one goals are already very strong. The first goal Lewy scored, the third goal we scored, was already excellent.
"The way he takes the ball down there and the way he locks up. Of course, he's had a bit of luck with that as well. But that's what distinguishes him, that he has this confidence in his quality.
"If I measure for goals now and I see that he has scored 34 goals in the Bundesliga this year, then you can think about how a player from the Bundesliga can become the Ballon d'Or winner. So why not? He has laid all the groundwork with this achievement this year and I would wish him well."
