Leonardo Jardim's Ligue 1 leaders were faced with a 5-3 deficit from the first leg at the Etihad Stadium but Mbappe was to the fore in a blistering opening – breaking the deadlock in the eighth minute and having another strike ruled out for offside.
Fabinho doubled Monaco's advantage and, although Leroy Sane briefly had City heading through on aggregate, Tiemoue Bakayoko's 77th-minute header sealed an unforgettable away goals triumph.
The thrilling nature of Monaco's progress to the quarter-finals will only boost Mbappe's stock as one of the most exciting youngsters in world football.
Anthony Martial became the most expensive teenager in history when he swapped Monaco for Manchester United in 2015 but the club's vice-president Vadim Vasilyev insists there is no desire to cash in on 18-year-old Mbappe, who would be well placed to shatter that record once more.
"Our intention is to keep Kylian Mbappe," Vasilyev told RTL.
"Mbappe is a product of our youth academy. He is our DNA. I am very proud.
"We have a real team. The first half was excellent – the sort of performance that the very top teams make."
Mbappe's goal against City at the Stade Louis II made it 11 in his past 11 appearances – form that could win him a maiden senior international call-up when Didier Deschamps names his France squad to face Luxembourg and Spain.