Corentin Tolisso, another new signing from French side Lyon, doubled the lead with a close-range header after the visitors failed to deal with a corner.
Bayern took an early lead when centre-back Niklas Sule headed in Sebastian Rudy's inswinging free-kick as the two summer arrivals from Hoffenheim combined.
Defending champions Bayern Munich opened the Bundesliga season with a comfortable XXXX win over Bayer Leverkusen on a rainy night at the Allianz Arena. At the other end Sven Ulreich denied both Karim Bellarabi and Kevin Volland with his feet.
Leverkusen almost equalised three minutes later but Sven Ulreich, still deputising for the injured Manuel Neuer, stuck out a boot to deny Admir Mehmedi.
Tolisso stung the palms of Leno four minutes into his league bow for Bayern as the champions made a dominant start.
Carlo Ancelotti's men remained in control of the proceedings after the restart.
The official was unsure Robert Lewandowski had been fouled but, after going to the video referees based in Cologne, he awarded a spot-kick and the Poland striker converted for 3-0.
Sydney schoolboy missing after splitting from family in Barcelona attack
After Ciutat de la Justicia, Andrew was expected to next go to the hospital where his wife is being treated for serious injuries. Seven-year-old Julian Cadman was separated from his mother during the Barcelona terror attack .
Dominik Kohr was one of the worst offenders in the Leverkusen attack, and spurned a brilliant chance to redeem himself for his myriad misses when presented with a free header just five minutes after Mehmedi's goal.
Heiko Herrlich's men pressed relentlessly for another goal but Bayern were able to protect their lead to the end to secure a vital victory in the first game of the season. It was nice for me, especially regarding the great atmosphere.
"It was not easy and we had a hard time".
"We played with courage up front and created numerous chances". The freshness was missing.
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"We left too much space between the lines".