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

Defender Kim Min-jae scored the only goal seven minutes before the interval, nodding home from close range after PSG goalkeeper Matvey Safonov had failed to deal with Joshua Kimmich's inswinging corner.

Ousmane Dembele, already on a yellow card for remonstrating with referee Istvan Kovacs in the first half, was sent off for a second bookable offence in the second when he caught Alphonso Davies with a late challenge.

Safonov produced a magnificent fingertip save to divert Jamal Musiala's effort on to the post as Bayern looked to establish a two-goal cushion late on, but Kim's header proved enough for the six-time winners.

It was a deserved victory for Vincent Kompany's side, who dominated possession at Allianz Arena and appear to be rediscovering their momentum in the competition after back-to-back defeats by Aston Villa and Barcelona.

The Bundesliga leaders started brightly and Musiala went close to opening the scoring with seven minutes on the clock, but shot straight at Safonov after collecting Kimmich's lofted ball into the penalty area.

Warren Zaire-Emery should have done better from Fabian Ruiz's cutback and Dembele forced a fine save out of Manuel Neuer in the first half, but PSG were once again made to rue their missed chances.

Harry Kane became the fastest player to reach 50 Bundesliga goals with his hat-trick against Augsburg on Friday evening, which lifted him to 20 goals in all competitions this season.

The England captain endured a frustrating first half in Munich, though, as he failed to an attempt on goal or a single touch inside the PSG box.

He did, however, almost set up Kingsley Coman for Bayern's second midway through the second period, but the French winger blazed his shot high over the crossbar.

The 31-year-old had a shot blocked by Willian Pacho not long afterwards as he missed the chance to add to his five Champions League goals this term.

It mattered not, though, as Bayern held on to their seventh straight victory in all competitions without conceding a single goal - the first time they have done so since September 2011 under Jupp Heynckes.

As for PSG, they have now managed only three goals in their five league-phase matches so far, despite going close on several occasions at Allianz Arena.

They finished the first half strongly and should have opened the scoring through Zaire-Emery, before the lively Dembele was denied by Neuer.

Dembele was unhappy with Kovacs' decision to brandish a second yellow card for his challenge on Davies, but it was a tackle the international - who was inside the Bayern penalty area at the time - did not need to make.

Watch highlights of every Champions League game from 22:00 on Wednesday on BBC iPlayer and the BBC Sport website and app.

There will also be a Champions League Match of the Day on BBC One on Wednesday, from 22:40 to 00:00.