Tobias Badila's own goal put the visitors ahead with Bernardo Silva doubling their lead before the break.
Thomas Lemar added a third four minutes from time as Monaco made it 98 league goals in 35 games so far this season.
Paris Saint-Germain had earlier beaten Bastia 5-0 to draw level on points with Monaco, who have a game in hand.
The Champions League semi-finalists boast a far superior goal difference to PSG and realistically need just one win from their final three matches to become champions for the first time since 2000.
Match ends, Nancy 0, Monaco 3.
Second Half ends, Nancy 0, Monaco 3.
Corner,  Monaco. Conceded by Guy N'Dy Assembe.
Attempt saved. Kylian Mbappe (Monaco) right footed shot from the left side of the box is saved in the bottom left corner. Assisted by Tiemoué Bakayoko.
Offside, Nancy. Guy N'Dy Assembe tries a through ball, but Youssouf Hadji is caught offside.
Attempt missed. João Moutinho (Monaco) right footed shot from outside the box is high and wide to the right. Assisted by Thomas Lemar.
Substitution, Monaco. Andrea Raggi replaces Bernardo Silva.
Goal!  Nancy 0, Monaco 3. Thomas Lemar (Monaco) left footed shot from very close range to the bottom left corner. Assisted by Kylian Mbappe.
Attempt missed. Amine Bassi (Nancy) right footed shot from outside the box is high and wide to the right.
Attempt missed. Kylian Mbappe (Monaco) left footed shot from a difficult angle on the left is close, but misses to the left. Assisted by Tiemoué Bakayoko.
Tiemoué Bakayoko (Monaco) wins a free kick on the left wing.
Foul by Issiar Dia (Nancy).
Substitution, Monaco. Kylian Mbappe replaces Valère Germain.
Attempt missed. Djibril Sidibe (Monaco) right footed shot from long range on the left is close, but misses to the left. Assisted by João Moutinho.
Attempt missed. Tiemoué Bakayoko (Monaco) header from the centre of the box misses to the left. Assisted by João Moutinho with a cross following a corner.
Corner,  Monaco. Conceded by Tobias Badila.
Attempt blocked. João Moutinho (Monaco) right footed shot from outside the box is blocked.
Delay over. They are ready to continue.
Substitution, Monaco. Tiemoué Bakayoko replaces Falcao.
Delay in match  (Nancy).
Attempt saved. Falcao (Monaco) right footed shot from outside the box is saved in the centre of the goal. Assisted by Fabinho.
Foul by Christophe Mandanne (Nancy).
Nabil Dirar (Monaco) wins a free kick in the defensive half.
Substitution, Nancy. Christophe Mandanne replaces Antony Robic.
Foul by Fabinho (Monaco).
Antony Robic (Nancy) wins a free kick in the defensive half.
Attempt blocked. Diallo Guidileye (Nancy) right footed shot from outside the box is blocked. Assisted by Amine Bassi.
Falcao (Monaco) wins a free kick in the attacking half.
Foul by Modou Diagne (Nancy).
Substitution, Nancy. Issiar Dia replaces Faitout Maouassa.
Attempt blocked. Bernardo Silva (Monaco) left footed shot from outside the box is blocked.
Corner,  Nancy. Conceded by Kamil Glik.
Corner,  Nancy. Conceded by Djibril Sidibe.
Foul by Fabinho (Monaco).
Diallo Guidileye (Nancy) wins a free kick in the defensive half.
Corner,  Monaco. Conceded by Modou Diagne.
Attempt blocked. Thomas Lemar (Monaco) right footed shot from the centre of the box is blocked.
Attempt saved. Valère Germain (Monaco) left footed shot from the centre of the box is saved in the centre of the goal. Assisted by Thomas Lemar with a through ball.
Djibril Sidibe (Monaco) wins a free kick in the defensive half.
Foul by Antony Robic (Nancy).
Monaco restored their three-point lead at the top of Ligue 1 thanks to a comfortable victory at relegation-threatened Nancy on Saturday.