Paris Saint-Germain have work to do if they are to qualify for the last 16 of the Champions League after a 1-0 defeat at Bayern Munich.

Kim Min-jae's first-half header proved decisive at Allianz Arena on Tuesday, with Ousmane Dembele's red card after the break making the task even tougher for PSG.

Having won just once in the competition so far – back in their opening game against Girona – Luis Enrique's team were second-best for much of the contest.

Bayern dominated the first half, with Kingsley Coman particularly dangerous, and the Bundesliga leaders got the goal their performance merited when Kim headed home from a corner in the 38th minute, with PSG's stand-in goalkeeper Matvey Safonov in no man's land.

Dembele, who had seen a decent attempt saved by Manuel Neuer in the first half, received his marching orders for a lunge on his France team-mate Coman just before the hour, with the referee deeming it worthy of a second booking. It marked the first time Dembele has been sent off since 2019, when he saw red for Barcelona in a LaLiga clash with Sevilla.

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

While Vincent Kompany's team are up to 11th in the standings, PSG are in 26th on just four points from their five matches, two places outside of the play-off spots with three games remaining.

Data Debrief: Kim off the mark for buoyant Bayern

Kim scored his first goal in the Champions League, in what was his 23rd appearance in the competition.

The scoreline ultimately flattered PSG, who finished with 0.88 expected goals (xG), while Bayern created 2.21 xG.

Bayern are now unbeaten in each of their last 33 home games in the Champions League group stage (W31 D2), the joint-longest such run in the competition's history, level with Barcelona between November 2009 and November 2020. They have gone on a run of seven wins without conceding for the first time since September 2011, too.

This is the eighth time in the Champions League that Bayern have defeated PSG, with only Real Madrid (11 vs Bayern) and Bayern themselves (10 vs Barcelona) winning more games against a single opponent in the competition's history.