Nemanja Radonjic skipped clear of the home defence to give Marseille the lead on 12 minutes, but Monaco equalised at the start of the second half through Guillermo Maripan's header.
Aurelien Tchouameni's first goal in the French top-flight put Monaco ahead before Stevan Jovetic's thumping free-kick in stoppage-time sealed a fifth victory in six games for Niko Kovac's resurgent team.
Arkadiusz Milik made his Marseille debut off the bench after signing on an 18-month loan from Napoli, but the Polish striker was unable to arrest his new club's slide as it lost a third league game in a row for the first time since April 2015.
It remains sixth and 13 points behind leader Paris Saint-Germain, while Monaco is closing in on the top three with just a point separating it and Lyon.
The latest setback is sure to create more uncertainty about the future of Villas-Boas, who had made it clear during the week he was not about to give up the fight with a tough run of fixtures on the horizon.
Marseille returns home to face Rennes next weekend, with a second meeting against Lens in a fortnight preceding the visit of bitter rival PSG to the Velodrome on 8 February (AEDT).