Bayern Munich boosted their hopes of finishing in the top eight in the league phase with a narrow victory over Paris St-Germain, who have been winless in the Champions League since September.

Defender Kim Min-jae scored the only goal seven minutes before halftime, nodding home from close range after PSG goalkeeper Matvey Safonov failed to deal with an inward corner from Joshua Kimmich.

Ousmane Dembele, who had already received a yellow card in the first half for speaking up to referee Istvan Kovacs, was sent off in the second half for a second bookable offense when he caught Alphonso Davies in a late foul .

Safonov made a superb fingertip save to keep Jamal Musiala’s shot off the post as Bayern tried to open up a two-goal lead in the closing stages, but Kim’s header was enough for a six-goal winner.

It was a deserved win for Vincent Kompany’s side, who dominated possession at the Allianz Arena and appear to be getting back into the swing of things after two defeats against Aston Villa and Barcelona.

The Bundesliga leaders got off to a bright start and Musiala almost opened the scoring after seven minutes, but shot straight at Safonov after intercepting Kimmich’s high-ball in the penalty area.

Warren Zaire-Emery should have done better after Fabian Ruiz’s cut and Dembele forced Manuel Neuer into a fine save in the first half, but PSG were once again left to rue their missed chances.