Bayern started the game on top but Dortmund steadied the ship and took the lead in the 27th minute through Jamie Gittens’ superb individual goal.
Second-half strikes from Valentin Rongier, Luis Henrique and Pierre-Emile Hojbjerg ensured Marseille remain third, nine points behind PSG and three off Monaco in second spot.
The 53-year-old recently extended his contract at the Etihad to 2027, but has said he will not overstay his welcome if results do not improve.
Aston Villa manager Unai Emery was happy with his players' response under pressure with their 3-2 victory over Everton in the Premier League.
Check out the live streaming details for Manchester United and Leicester City Premier League 2024-25 match to be played at Old Trafford.