PARIS (AP) — Titleholder Paris Saint-Germain trailed early, led by three goals and ultimately held on for a pulsating 5-4 win over Bayern Munich in the highest-scoring semifinal match in Champions League history on Tuesday.

And there’s still next week’s second leg to come.

PSG built a 5-2 lead early in the second half thanks to two goals each from flying winger Khvicha Kvaratskhelia and Ousmane Dembélé at Parc des Princes.

“We deserved to win, we deserved to lose, we deserved to draw,” PSG coach Luis Enrique said. “It was an exceptional match, I have never experienced a match of such intensity as a coach. I have never seen a rhythm like that, it was incredible, you have to congratulate all the players.”

Down by three goals, Bayern fought back brilliantly.

Defender Dayot Upamecano’s header midway through the second half from Joshua Kimmich’s free kick gave Bayern hope and Luis Díaz’s stinging strike made it a one-goal deficit heading into next Wednesday’s return leg in Munich.

“I think something special can happen at home, there will be 75,000 people, it will be a hell of an atmosphere,” Bayern coach Vincent Kompany said. “The Allianz Arena is a mythical area where Bayern has enjoyed much success.”

Rather than scale back and defend more, Kompany said he was ready to take even more risks.

“There is no middle ground,” he said. “We will give everything, everything, everything we have. We’re waiting for them, we want this.”

Kompany was suspended and watched from the stands, so assistant Aaron Danks took over on the touchline as Bayern lost for the first time in any competition since Jan. 24.

Harry Kane’s penalty gave Bayern the lead in the 17th minute and Kvaratskhelia equalized soon after for PSG. Midfielder João Neves — who is 5-foot-7 — then headed PSG ahead from a corner.

A dramatic first half saw Michael Olise equalize for Bayern after bursting into the area before Swiss referee Sandro Schärer awarded a penalty for PSG when a video review spotted a handball from Canada defender Alphonso Davies.

PSG’s penalty was contested by Bayern’s players. Davies turned his body to Dembélé’s right-wing cross but the ball bounced off his hip and hit his arm. Although Davies was turning away from play he failed to keep his hands behind his back.

“The rules about handball change every week,” Kompany said. “The ball hits the body then the hand and you give a penalty, I don’t agree.”

Dembélé fired the penalty past Manuel Neuer — who guessed the right way — to send PSG ahead 3-2 at the break.

“Two great teams who attack and don’t question themselves,” Dembélé said. “It was an incredible match, but now we go to Munich to qualify. We won’t change our way of playing, and it will be two teams who attack.”

Bayern started well.

Moments after PSG defender Marquinhos was shown a yellow card for stopping Díaz in his tracks, the left winger earned a penalty when he was fouled by Willian Pacho, and from the spot Kane beat goalkeeper Matvey Safonov for his 13th goal of the competition — two behind Real Madrid’s Kylian Mbappé — and 54th goal of another prolific season.

Safonov made a good save moments later from Olise, then Dembélé missed a one-on-one.

PSG equalized in the 24th when Désiré Doué’s pass found Kvaratskhelia on the left and the Georgia star cut inside before curling the ball into the bottom right corner for his 10th goal of the competition.

Dembélé and Doué missed further first half-chances from counterattacks which exposed Bayern’s tactic of playing with a perilously high defensive line.

The lesson was not heeded in the second half as PSG scored twice from rapid counterattacks.

Kvaratskhelia rifled in a powerful shot in the 56th after running onto a ball across the area that eluded all the defenders and Bayern’s poor defending was exposed again two minutes later. Doué was given far too much room before feeding Dembélé on the left, and he scored with a low shot off in the post for a 5-2 lead.

“You were standing on the field going ‘what’s going on here?’ because we definitely weren’t three goals worse,” Kimmich said. “It was important that we stayed relatively calm.”

But at the end, PSG was struggling and Pacho headed Kimmich’s looping header off the line with seconds remaining in stoppage time.

“It was a very, very intense game,” Bayern defender Jonathan Tah told Prime Video. “We showed what sort of a team we are, that we can cope with adversity and also with difficult refereeing decisions.”

Luis Enrique was exhausted just watching.

“I’m so tired, and I didn’t run a single kilometer,” he said. “So I don’t how the players are feeling.”

He does not expect any respite next week.

“I just asked my staff ‘ how many goals do you think we will need to win this match?’ They said ‘minimum three.’ Bayern Munich in their stadium are even stronger but we will try and show the same mentality.”

Spanish side Atletico Madrid hosts London club Arsenal on Wednesday in the other semifinal first leg. The final will be played in Budapest, Hungary on May 30.

AP Sports Writer James Ellingworth in Düsseldorf contributed.

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