Bayern, who host Liverpool on Wednesday in their Champions League, last 16, return leg clash after a goalless draw at Anfield, went top on goal difference from Dortmund, who needed late goals to win 3-1 at home to Stuttgart.
The excellent James Rodriguez scored Bayern's third early in the second half, before substitute Franck Ribery set up Mueller, Joshua Kimmich, and Lewandowski to complete the rout.
Gladbach stay fourth, level on 47 points with Leipzig, and both clubs lag nine points behind new leaders Bayern and Dortmund.
On Friday: Serie A: Juventus 4 (Kean 11, 39, Can 67-pen, Matuidi 71) bt Udinese 1 (Lasagna 84).
"We are now where we wanted to be", Bayern coach Niko Kovac said.
Arnold - whose Wolfsburg side travel to the Allianz Arena on Saturday - does not believe a seventh consecutive Bundesliga title for Bayern would be healthy for the game in Germany, and he therefore wants to see Lucien Favre's side triumph this season.
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The 30-year-old Lewandowski went into the match with 74 goals in 131 league games at Borussia Dortmund, and 121 in 149 with Bayern.
Borussia Dortmund spent almost six months atop the Bundesliga table and it looked like they would finally be ending Bayern Munich's dominance by lifting the Salatschüssel this season.
"We could and should have scored more goals".
Lewandowski is also now the Bundesliga's top goalscorer having netted 17 league goals so far this season and gave a positive response when asked whether he could end his career with Bayern.
Bayern's Robert Lewandowski scored a brace as they beat Wolfsburg in Bundesliga action on Saturday.
Christian Pulisic's introduction with just over 10 minutes remaining made the difference for Dortmund, which was pegged back after Castro whipped in a free kick for Marc Oliver Kempf to equalize with a header in the 71st.