Bayern Munich battled past 10-man Paris Saint-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.

It was the second straight win for Bayern in the competition after a rocky start of one victory and two defeats, lifting them to 11th with nine points from five games, a point off the top eight places that bring automatic qualification for the last 16.

Luis Enrique's PSG are 26th on four, outside the playoff spots with three matches remaining in the first phase.

Bundesliga leaders Bayern, who visit Borussia Dortmund on Saturday before next week's German Cup last-16 clash at home to holders Bayer Leverkusen, had the better start against PSG and two early opportunities through Jamal Musiala and Leroy Sane.

The visitors responded with a double chance of their own, but neither Ousmane Dembele, who was sent off just before the hour mark, nor Joao Neves could beat goalkeeper Manuel Neuer.

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 keeper Matvei Safonov fluffed a corner in the 38th minute.

Before the French side's defence had time to recover Bayern almost scored a second five minutes before halftime with Kingsley Coman firing over the bar after a solo run.

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

Bayern tried to make the most of the extra man, piling pressure on the visitors, and Coman came close again in the 66th minute, narrowly missing the target after a quick passing move.

Safonov made amends for his earlier mistake by tipping a 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.