France international Coman appeared at the back post to head home in the 59th minute, completing a sweeping move from Bayern.
Coman's strike secured a treble for the Germans and punished PSG's wastefulness in the first half as Neymar and Kylian Mbappe both failed to beat Bayern keeper Manuel Neuer from close range.
PSG were playing in their first European Cup final after billions of euros of investment from the Qatar royal family but they fell short on the final step to glory.
