PSG led 5-2 early in the second half on Tuesday (Wednesday AEST) thanks to two goals each from flying winger Khvicha Kvaratskhelia and Ousmane Dembele at Parc des Princes.
"Two great teams who attack and don't question themselves," Dembele said.
"We know Bayern is a big team, but so are we. At 5-2 we stopped playing a bit. 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."
Defender Dayot Upamecano's header midway through the second half from Joshua Kimmich's free kick gave Bayern hope, and Luis Diaz's stinging strike made it a one-goal deficit heading into next Wednesday's return leg in Munich.
"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."
Harry Kane's penalty gave Bayern the lead in the 17th minute, and Kvaratskhelia equalised soon after for PSG.
Midfielder Joao Neves - who is just 170cm tall - then headed PSG ahead from a corner.
A dramatic first half saw Michael Olise equalise 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 Dembele'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.
Dembele fired the penalty past Manuel Neuer - who guessed the right way - to send PSG ahead 3-2 at the break.
Moments after 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 54th goal of another prolific season.
Safonov made a good save moments later from Olise, then Dembele missed a one-on-one.
PSG equalised in the 24th minute when Desire Doue'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.
Dembele and Doue missed further first half-chances from counterattacks that exposed Bayern's tactic of playing with a perilously high defensive line.
But at the end, PSG were struggling and Pacho headed Kimmich's looping header off the line with seconds remaining in stoppage time.
Spanish side Atletico Madrid host London club Arsenal on Wednesday in the other semi-final first leg.
