"We played really well and controlled the game from the first minute," said Lewandowski.
"Everything worked out like we had planned it. When we're so flexible on the pitch, it makes it hard for any opponent to stop us."
Lewandowski has now netted 82 goals for Munich amidst reports he wants to join Real Madrid next season, but Bayern chairman Uli Hoeness laughed off the claim by Spanish newspaper AS.
"It's not April 1," quipped Bayern boss to broadcaster Sport1.
The rout left Bayern second in Germany's top flight, a point behind Hanover 96, who claimed the lead after four games with a 2-0 win over Hamburg on Friday.
This was a much improved performance from Bayern compared to last Saturday's 2-0 defeat at Hoffenheim and Tuesday's lacklustre 3-0 win at home to 10-man Anderlecht in the Champions League.
"I'm happy. We had good combinations and created good chances. We did well," said Bayern coach Carlo Ancelotti.
Arjen Robben had slammed Bayern's performance against the Belgians, while Lewandowski had added to the unrest by criticising the club's spending policy.
That came after Thomas Mueller had complained about being benched for the 2-0 win at Werder Bremen.
However, all three scored against Mainz at Munich's Allianz Arena on Saturday.
Mueller opened the scoring after just 11 minutes when he drilled home Robben's pass on Bayern's first attack.
The flying Dutch winger added a second on 23 minutes when Joshua Kimmich's pass put him in behind the defence and he drilled his shot home.
Lewandowski then doubled the damage with two superb goals.
Kimmich released Mueller on the right wing, who put in a superb cross for the Poland striker to convert on 50 minutes.
Lewandowski grabbed his second and Bayern's fourth goal when he headed across Mainz's former Germany goalkeeper Rene Adler.
Franck Ribery started on Bayern's bench having thrown his shirt away in disgust after being substituted late against Anderlecht.
Borussia Dortmund can go top of the table on Sunday if they beat Cologne at home on Sunday.