Icardi struck the opening goal inside two minutes at the Parc des Princes before teenage Saint-Etienne defender Wesley Fofana was dismissed for a second booking on the half-hour.
PSG ruthlessly capitalised on their man advantage as coach Thomas Tuchel elected to field all four members of his fearsome attacking quartet - Icardi, Neymar, Kylian Mbappé and Angel Di Maria - against a side decimated by injury and illness.
"I am convinced that Icardi and Mbappé love to play together," said Tuchel.
"We talk about the four attackers but we are a team with 11 players. Neymar, for example, helps Juan Bernat. That's the sort of spirit which we need to be dangerous. We have the best players but we also have the best team".