PSG host relegation battling Le Havre on Saturday
French prodigy Mbappe and Colombia striker Falcao scored in the third and 17th minutes before Marco Reus gave the visitors hope with a 48th-minute goal, only for substitute Valere Germain to wrap up the win for the French side nine minutes from time.
Monaco joined Real Madrid, Atletico Madrid and Juventus in the last four of Europe's premier cub competition.
The incident occurred a week after the first leg was postponed by 24 hours after the Borussia team bus was attacked with explosives on its way to the stadium.