Bayern Munich battled past 10-man Paris St Germain 1-0 in the Champions League thanks to Kim Min-jae's winner on Tuesday to improve their chances of automatic qualification and leave the visitors in trouble after a third loss in the competition.

With PSG's only win so far coming against Girona in their opener they were desperate for points but Bayern struck first with South Korea's Kim heading home from close range after goalkeeper Matvei Safonov fluffed a corner in the 38th minute.

Things got worse for Luis Enrique's PSG when Ousmane Dembele was dismissed for lunging tackle that brought a second booking in the 57th, leaving an already struggling side with 10 men.

Safonov made amends for his earlier mistake by tipping a Jamal Musiala shot onto the post but despite some late pressure PSG could not prevent Bayern claiming a seventh consecutive victory and seventh straight clean sheet in all competitions.

The Bavarians climbed to 11th with nine points from five games, a point off the top eight places that bring automatic qualification for the last 16. PSG are 26th on four, outside the playoff spots with three matches remaining in the first phase.