Bundesliga champions Bayern dominated at Berlin’s Olympic Stadium as David Alaba smashed home an early free-kick before Serge Gnabry added the second goal in the first-half.
Lewandowski has 51 goals in total this season after scoring twice in the second-half either side of a Sven Bender header for Leverkusen. Kai Havertz converted a penalty deep into added time for Leverkusen.
“In the second half we showed that we are the better team and wanted to be cup winners,” said man-of-the-match Lewandowski.
Bayern, crowned Bundesliga champions for the eighth straight year last Saturday, have won all of their 11 games since the season resumed in mid-May after a two-months hiatus due to the coronavirus.
They could finish the season winning the treble as they are among the favourites for the Champions League finals in Lisbon next month. This was the 13th time in the club’s history they have won the double.
Lewandowski, crowned Bundesliga top-scorer for the fifth time last weekend, netted six times in the cup, has 34 league goals and 11 more in the Champions League this season.
Leverkusen completed a hat-trick of defeats after also losing the 2002 and 2009 cup finals in Berlin.
When Lewandowski was clattered by defender Edmond Tapsoba on 16 minutes, it was Alaba who swung the resulting free kick inside the post to give Bayern the opening goal.
They doubled their lead after Joshua Kimmich won the ball in midfield eight minutes later.
His pass split the defence, Gnabry sprinted onto the ball and fired past Leverkusen goalkeeper Lukas Hradecky to make it 2-0 at the break.
“We are so happy that we got the double. In the first half we had the game completely under control,” said Gnabry.
With players’ calls echoing around the near-empty terraces of the cavernous stadium, where Germany head coach Joachim Loew was one of a handful of guests, the game was played in an eerie atmosphere.
“It’s a bit of a sad moment,” admitted Bayern forward Thomas Mueller, who lamented the lack of fans, after winning the German Cup for the sixth time in his career.
“If the fans are missing at such a cup final, it’s not the same. We’ve done well this season over long stretches, but it also hurts a bit.”
Having skied a shot at goal moments earlier, Lewandowski made it 3-0 when he controlled a clearance kick by goalkeeper Manuel Neuer and tried a long-range speculative shot at Hradecky.
The Leverkusen keeper parried the shot, but watched in horror as it rolled behind him and over the goal line on 59 minutes.
“I noticed that the goalkeeper was a bit off his line, so I thought I’d just give it a try,” revealed Lewandowski.
“It was a little surprise it went in, but you always have to try.”
It fired life into Leverkusen, whose centre-back Sven Bender slipped his marker Leon Goretzka and headed home on 64 minutes.
Leverkusen nearly got a second moments later when Kevin Volland and Havertz both failed to connect with a cross.
Lewandowski claimed his second when he fired home Ivan Perisic’s pass on 89 minutes.
Bayern defender Alphonso Davies conceded the penalty in the fourth minute of added time which Havertz converted just before the whistle.