Bayern took the lead in the 17th minute after Harry Kane scored from the penalty spot. But PSG responded quickly, with Khvicha Kvaratskhelia equalising before Joao Neves headed them in front.
The German side fought back, with Michael Olise making it 2-2 before halftime. However, PSG regained the lead in added time when Ousmane Dembele scored from the penalty spot after a handball by Alphonso Davies.
PSG came out stronger in the second half. Kvaratskhelia scored his second goal to make it 4-2, and Dembele added another soon after to give the hosts a 5-2 lead.
Bayern did not give up. Dayot Upamecano pulled one back with a header, and Luis Diaz later scored to reduce the gap to 5-4.
Despite late pressure from Bayern, PSG held on for the win.
The match was also special for PSG coach Luis Enrique, who became the fastest manager to reach 50 Champions League wins, doing so in 77 matches. He beat the record of Pep Guardiola.
Dembele stood out for PSG, becoming only the second player from the club to score and assist in a Champions League semi-final, after Angel Di Maria.
PSG now take a slim lead into the second leg in Germany, where Bayern will hope to turn things around.
