Bayern quickly got into their stride and Suele got the home side off to a flying start when he headed in a free-kick from Sebastian Rudy.
The referee initially waved away claims for a penalty, but after consulting with video review, Bayern were awarded the spot-kick, which the Poland global confidently tucked home to make it 3-0.
Bayern could have taken the lead after five minutes when Frenchman Tolisso, the club's record signing at 41 million euros (37.46 million pounds), came close to scoring on his league debut but goalkeeper Bernd Leno did well to block his low drive.More news: Why CEOs spurned Donald Trump's business councils, in their own words
Bayern boss, Carlo Ancelotti said following the game: "It was a hard match".
Although the score-line suggested a comfortable victory for Bayern Munich, Leverkusen made sure they had to fight for the three points at a rain drenched Allianz Arena. At the other end Sven Ulreich denied both Karim Bellarabi and Kevin Volland with his feet. They were able to extend their advantage after Robert Lewandowski converted a foul play penalty to make it 3-0 on the scoreboard in the 57th minute.
Substitute Julian Brandt set up Admir Mehmedi for Leverkusen's deserved equalizer.
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. "But I will decide on the lineup tomorrow", Ancelotti said. That was nice for me in front of a great stadium. It wasn't easy, we struggled. In the first half we had good chances. The freshness was missing. "Perhaps the scoreline is a little too high".