Falcao scores double as Monaco hit six
Falcao's goals, the second of which came from the penalty spot, were followed by a Kylian Mbappe strike moments after his second-half introduction.
Guido Carrillo added two late goals either side of a Fabinho penalty as the principality club moved clear in second place in Ligue 1, three points behind leaders and local rivals Nice.
The win also underlined Monaco's status as the most prolific side in Europe's big five leagues - they are averaging three goals a game after 12 matches and have scored at least six goals on three occasions since the start of October.
It was all too much for Nancy, who are on the brink of being bought out by a Chinese consortium but also languish in the relegation zone.
Falcao had scored twice in Monaco's 3-0 Champions League win at home to CSKA Moscow in midweek and was back among the goals in the 25th minute, nodding in from inside the six-yard box after Michael Chretien had turned the ball against his own bar.
He netted a penalty five minutes later after Fabinho had gone down in the box under a Dialo Guidileye foul, and the Colombian now has eight goals in 10 appearances altogether this season.
He even had the ball in the net again just before half-time, but this time his effort was ruled out for an offside against Valere Germain.
Leonardo Jardim's side are anything but dependent on Falcao, however, as their second-half display showed.
Seventeen-year-old starlet Mbappe replaced Germain just after the hour and required only two minutes to add his name to the scoresheet, rolling in the loose ball after goalkeeper Guy Roland Ndy Assembe had turned out a Benjamin Mendy cross.
Falcao then made way for the Argentine forward Carrillo, who got number four three minutes from time, heading in a cross from the left by the marauding Mendy.
The hosts got number five when Brazil international Fabinho tucked away another penalty following a Clement Lenglet foul on Corentin Jean.
But they were not done there, making it 6-0 in stoppage time as the exciting Mbappe set up Carrillo for his second of the day.
Unfortunately for Monaco, their performance was played out in front of a desperately sparse crowd in the principality, but they are a real threat to leaders Nice who put their unbeaten league record on the line when they visit Caen on Sunday.
Champions Paris Saint-Germain, six points adrift of Nice in third, host Rennes on Sunday.
On Friday Marseille were beaten 3-1 at Montpellier, leaving new coach Rudi Garcia still without a win after three games in charge.