Three days after their teams played out a 3-3 draw at Parc des Princes, coaches Thomas Tuchel and Robert Moreno clashed on the touchline at Stade Louis II in a rearranged match.
An end-to-end start was capped off by Mbappe resuming his scoring run, though VAR should have awarded Monaco a penalty shortly after the restart.
Monaco's frustration with the officiating was compounded in first-half stoppage time as Neymar scored his second penalty in as many matches after a blatant dive from Layvin Kurzawa.
Pablo Sarabia's strike increased PSG's lead - though only after a VAR review - with Tiemoue Bakayoko scuffing in a consolation goal before Mbappe doubled his tally in stoppage time.
Both teams picked up where they left off after Sunday's thrilling encounter in Paris, Keylor Navas and Benjamin Lecomte making excellent stops before Mbappe slotted home in the 24th minute.
A lengthy VAR check for a possible foul and offside frustrated PSG, and Gelson Martins would have equalised immediately if not for Navas, though the hosts were furious that they were not awarded a penalty for an apparent handball by Presnel Kimpembe prior to the shot.
And, after Lecomte had made a fantastic save from Mbappe and Colin Dagba had a goal disallowed for offside, Monaco felt let down by more poor officiating.
Kamil Glik stood his ground heading into a challenge with Kurzawa, who clearly initiated the contact on the byline, yet VAR did not overturn the referee's decision to award PSG a penalty, which Neymar converted.
Wissam Ben Yedder should have done better at the end of a superb move midway through the second half, but the contest was settled when Sarabia volleyed in a minute after coming on.
Navas' mistake did allow Bakayoko to bundle in a deserved goal for Monaco, yet it was Mbappe who had the final say when he raced through to add his second, this time celebrating against his former club after not doing so first time around.