The German Cup holders started their title defence with Lewandowski establishing a 3-0 lead within 43 minutes before Arturo Vidal and Mats Hummels rounded off the 5-0 scoreline, reports Xinhua.
Breaking the deadlock just three minutes into the game, Lewandowski made use of Franck Ribery's build-up play to slot home a follow up shot from close range.
Jena were unable to respond as Bayern dictated the proceedings on the pitch. Lewandowski doubled the lead after lobbing a through ball, again from Ribery, over onrushing Jena custodian Raphael Koczor on 34 minutes.
The Poland international wasn't done with the scoring as he wrapped up his hat-trick after drilling the ball from the edge of the box into the bottom left corner in the 43rd minute.
After half-time, Jena tried to pile on the pressure but Bayern goalkeeper Manuel Neuer was on guard to block Manfred Starke's free-kick three minutes into the second half.
As the match progressed, Bayern increased pressure to extend the lead as Arturo Vidal poked home Lewandowski's square pass into the open goal in the 72nd minute before Mats Hummels rounded off the expected first round victory five minutes later.
