Argentine Icardi put the holders in front by bundling the ball into the net in the ninth minute, while France striker Mbappe doubled their advantage from the penalty spot shortly before half-time.
Lille, who lead PSG at the top of the Ligue 1 standings by three points, were awarded a penalty in the second half which would have given them hope of clawing their way back into the Cup tie.
But PSG keeper Keylor Navas saved Yusuf Yazici's spot kick, a week after keeping out a penalty from Barcelona's Lionel Messi in the Champions League, and Mbappe rounded off the victory for the hosts by striking again in stoppage time.
Angel Di Maria and Marquinhos both started for PSG three days after their homes were broken into by burglars while their families were in.
Di Maria helped set up the opening goal, whipping a cross into the box which deceived Lille defender Tiago Djalo and keeper Mike Maignan, allowing Icardi to walk the ball over the line.
Icardi sustained an injury late in the first half but PSG had the luxury of bringing on Mbappe, who earned the penalty by drawing a foul from Lille defender Mehmet Zeki Celik before smashing home from the spot.
PSG defender Layvin Kurzawa offered Lille a chance when he handled in the area but Costa Rican Navas got down low to parry the shot, saving a third spot kick of the season.
PSG coach Mauricio Pochettino paid tribute to Di Maria and Marquinhos for playing.
"It's been a difficult few days for the players and their families, they were very affected by what happened, no-one is prepared for situations like that," he said.
"I congratulate them both as they did a great job of staying focused, they showed an extraordinary mentality."