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 Mbappe and Angel Di Maria — against a side decimated by injury and illness.
“I am convinced that Icardi and Mbappe 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.”
Neymar doubled the lead with a nonchalant chipped finish over goalkeeper Jessy Moulin, who scored a comical own goal on the stroke of half-time.
Di Maria’s low cross was hacked by Timothee Kolodziejczak into the legs of team-mate Loic Perrin, the ball rolling back off the post before hitting Moulin and trickling over the line.
The hosts bagged a fourth when Mbappe rounded Moulin and cut back for Icardi to add to his tally, and he completed his hat-trick when the former raced clear before selflessly presenting the Argentine with a tap-in.
The pair reversed roles for the sixth goal, Icardi controlling superbly and sliding across goal for a lunging Mbappe to turn home from close range.
Former PSG midfielder Yohan Cabaye hit a consolation goal for Saint-Etienne when he headed in the rebound after his second-half penalty was saved by Sergio Rico.
PSG have now scored at least four goals in their past six matches. The record eight-time champions will discover their semi-final opponents when the draw is made on Thursday.
Lyon battled into the last four with a 3-1 victory at home to Brest.
Moussa Dembele broke the deadlock on 19 minutes and Houssem Aouar added a second shortly after half-time for Rudi Garcia’s side.
Samuel Grandsir gave Brest hope with a tidy finish five minutes from time but Jean Lucas made sure of the win with a firm 20-yard drive in stoppage time.
Luiz Araujo and Victor Osimhen were on target as Lille overcame Amiens 2-0.
Reims eliminated holders Strasbourg on Tuesday after winning 4-2 on penalties following a goalless draw.
The competition, which includes all the clubs from France’s top two divisions and a handful of teams from the third tier, will be suspended indefinitely at the end of this season.