Bastia supporters arrived on a ferry with hopes of causing an upset against the promoted side, whose investment looks to make them Paris St Germain's biggest rivals for the title.
However Emmanuel Riviere gave Monaco a 39th-minute lead, and when Falcao's powerful finish two minutes later gave the home side a second it was clear which way the match would go.
Falcao put the finishing touches to the victory in the 89th minute.
It meant PSG's two-hour spell at the top was abruptly ended, the capital side having kicked off earlier in the evening in their match at Valenciennes but finishing the day where they began, two points off the summit.
Edinson Cavani scored as Laurent Blanc's team kept up the pressure at the top of the table and heaped further misery on Valenciennes manager Daniel Sanchez with a 1-0 win.
The goal came in first-half stoppage time, via a pass from Zlatan Ibrahimovic, and, like Monaco, the Parisians remain unbeaten after seven rounds of games. Valenciennes have just three points so far.
Lyon's revival suffered a setback on Wednesday evening as Fabrizio Ravanelli's Ajaccio sent them stumbling to a 2-1 loss.
Unbeaten in three, after a run of four defeats, Lyon headed to Corsica with another productive evening in mind, but it was a tough experience at the Stade Francois Coty where Salim Arrache and substitute Aboubacar Camara scored either side of Steed Malbranque's equaliser.
Arrache netted in the 18th minute, Malbranque's leveller came in the 56th minute, and Camara's clincher arrived with 20 minutes remaining to earn Ajaccio their first win of the season.
Lyon's disappointing night was compounded by the stoppage-time dismissal of Alexandre Lacazette for a second bookable offence.
Goals by Filip Djordjevic and Fernando Aristeguieta guided Nantes to a 2-0 home victory over Nice, while a second-half effort from Martin Braithwaite clinched a first home win of the Ligue 1 season for Toulouse as Lorient went down 1-0.
Bordeaux and Reims failed to muster a goal between them at the Stade Chaban-Delmas, but Guingamp and Sochaux served up six, hosts Guingamp winning 5-1.
Jocelyn Gourvennec's home side raced ahead thanks to strikes from Christophe Mandanne, Claudio Beauvue and Fatih Atik.
Substitute Cedric Bakambu reduced the deficit for bottom-of-the-table Sochaux two minutes after half-time, but Younousse Sankhare snuffed out any remote hopes of a comeback 20 minutes from time and then Steeven Langil rounded off the resounding win.