Mbappe was on target in the 24th and 90th minutes with Neymar tucking away a penalty in first-half stoppage time.
Pablo Sarabia added another in the 73rd minute, just seconds after coming on as a substitute.
Ibrahima Bakayoko grabbed a late consolation for Monaco, beating the impressive Kaylor Navas in goal.
"In every area, we were better than Sunday," said PSG coach Thomas Tuchel.
"It's a deserved victory, we had lots of possession."
Tuchel fielded his 'Fab Four' attacking stars in Mbappe, Neymar, Mauro Icardi and Angel Di Maria.
It was a decision which paid dividends when Di Maria floated over a cross for Mbappe to score the opener.
Monaco goalkeeper Benjamin Lecomte denied Mbappe on two further occasions in the first half.
Neymar made it 2-0 from the penalty spot in injury-time after Kamil Glik had fouled Layvin Kurzawa.
Sarabia's goal was set-up by fellow substitute Marco Verratti before Mbappe completed the rout of the club he had joined in 2015.