The centre-back scored after an error from PSG goalkeeper Matvei Safonov, starting ahead of Gianluigi Donnarumma, who spilled the ball into Kim's path.

The South Korean's effort was enough to decide the rematch of the 2020 Champions League final -- won by Bayern by the same scoreline -- and all but extinguishes PSG's hopes of a top-eight finish and avoiding the playoff round.

Ousmane Dembele picked up a second yellow for an unnecessary challenge with half an hour remaining, with Bayern successfully shutting up shop as a result.

With just three games remaining, even making the knockouts is not a given for the French champions, who are in 26th spot -- two outside the playoff placings.

PSG host Manchester City in January along with facing tricky away trips to Red Bull Salzburg and Stuttgart.

Bayern's top-eight hopes look rosier after the win, which extended their run of clean sheets to seven straight games in all competitions.

Bayern now sit 11th and take on relative European minnows Shakhtar Donetsk, Feyenoord and Slovan Bratislava in their remaining games.

Both sides came into the game unbeaten and six points clear in their domestic leagues but in dire need of points in Europe.

Bayern coach Vincent Kompany opted for the speed of Leroy Sane over the creativity of France winger Michael Olise up front.

PSG boss Luis Enrique made five changes to his side but most notable was his decision to stick with goalkeeper Safonov, rather than Donnarumma, who had played all but one Champions League game this season.

Luis Enrique defended his call before the game, telling reporters: "I make my choices based on what I see on the pitch and what's best for the team."

The decision appeared to pay off early, with Safonov responsible for good saves from Jamal Musiala and Sane inside the opening 12 minutes.

Kingsley Coman, the PSG academy product who scored the only goal in the 2020 final, almost broke the deadlock shortly afterwards, dribbling through five defenders and blasting just wide.

After PSG had a few opportunities of their own, including Joao Neves' long-range effort whistling past the goalpost on 33 minutes, the Russian goalkeeper made a mistake which led directly to the opener.

Joshua Kimmich swung in a corner on the 38-minute mark which Safonov spilled.

And Kim took advantage to power a header into the net for the first Champions League goal of his career.

Bayern were happy to let the game come to them in the second half but Dembele's second yellow -- his first had come for dissent -- took the steam out of PSG's hopes of a comeback.