Niklas Sule and Corentin Tolisso struck in the first half, as the Polish striker netted in the second period before Admir Mehmedi scored for Leverkusen
The video assistant referee is being trialled in the Bundesliga this season and came into play for the first time to spot that Lewandowski was fouled in the area in the second-half.
Summer signing Niklas Sule netted the opener in the ninth minute with a deft header
The Bayern Munich players celebrate the defender netting the opener at the Allianz Arena
The Polish striker dutifully slotted home the penalty to put Bayern 3-0 up after new signings Germany defender Niklas Sule and France midfielder Corentin Tolisso scored with first-half headers.
Leverkusen deservedly pulled a goal back at 3-0 down when Swiss striker Admir Mehmedi capped off a bright passage of play with a fierce shot.
Sule said of the match: “That was a special day for me – my first game for my new club and my first goal, that was nice.”
Leverkusen’s Germany defender Jonathan Tah was left ruing his side’s poor first-half display.
Tah said: “We were asleep in the first half and conceded stupid goals.”
On a dramatic opening night, the start of the second half was also delayed by 15 minutes as torrential rain swept the stadium.
Former Lyon midfielder grabbed the second goal of the evening against Bayer Leverkusen
The French international reacts after his close range header finds the bottom right corner
Having won last season’s German league title – their fifth in a row by 15 points, the thumping win in Munich suggests Bayern are in no mood to relax their iron-grip on the Bundesliga title.
The hosts were missing a host of injured stars at Munich’s rain-lashed Allianz Arena including new club captain Manuel Neuer, defender Jerome Boateng and new-signing James Rodriguez.
Nevertheless, it took just nine minutes for Bayern to go ahead.
Centre-back Sule nodded Sebastian Rudy’s free-kick past his Germany teammate – Leverkusen goalkeeper Bernd Leno.
Bayern doubled their lead when the club’s record signing Tolisso, who cost £40million from Lyon, headed home on 18 minutes when Arturo Vidal found him in the box.
Tolisso could have scored again soon after when he hit the post.
Torrential rain then forced the start of the second-half to be delayed by 15 minutes.
Robert Lewandowski converted a second half penalty after the spot-kick was awarded by a video assistant referee
The Polish star celebrates after putting the Bundesliga side 3-0 up
The stadium briefly emptied in the break as supporters sought shelter before resuming their soaking wet seats.
Leverkusen’s new coach Heiko Herrlich responded to his side’s woeful defending in the first half with two changes for the second 45 minutes.
Germany winger Julian Brandt replaced Jamaica’s Leon Bailey and defender Aleksandar Dragovic replaced new signing Sven Bender at centre-back.
It changed little and when Chile international Charles Aranguiz pulled Lewandowski to the floor as Bayern attacked, the VAR spotted the foul and the Polish striker converted the resulting spot kick on 53 minutes.
Moments later, Neuer’s understudy Sven Ulreich proved his worth in the Bayern goal to deny Brandt, then Dominik Kohr in quick succession.
With an hour played, Bayern’s stand-in captain Thomas Mueller made way for Arjen Robben.
Leverkusen showed heart when Brandt’s pass found Mehmedi unmarked on 65 minutes and the Swiss international slotted home their consolation.
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