The win leaves Bayern Munich two points clear of second-placed RB Leipzig with Borussia Dortmund third, three points behind the leaders.
Bundesliga: Robert Lewandowski has scored 10 goals in five league starts for Bayern Munich, while Borussia Dortmund's Erling Braut Haaland has scored five times.
Robert Lewandowski converted a first-half penalty, then headed home a second as Bayern Munich roared back from conceding an early goal to claim a convincing 6-2 win in Austria.
Thomas Mueller, 31, converted an early penalty to put the visitors on the way to a success which saw him match the tally of legendary goalkeeper Oliver Kahn on 260 league wins.
Champions League: Having slumped to a 3-1 defeat away to Lazio in their opening game last week, Borussia Dortmund were under pressure to pick up three points.
Lionel Messi and Cristiano Ronaldo are now set to renew their individual rivalry when Barcelona and Juventus clash in Group G.
The former Borussia Dortmund coach replaced Brendan Rodgers as the man in charge of Liverpool.
Mario Goetze, who was a free agent after Borussia Dortmund allowed him to leave, has signed a contract with Dutch club PSV Eindhoven.
Footage emerged of Tammy Abraham attending a party with England teammates Ben Chilwell and Jadon Sancho in an apparent breach of national coronavirus rules.
Jadon Sancho scored 17 goals in the Bundesliga last season, and is currently being sought after by Manchester United.