He opened the scoring from six yards out seconds after coming off the bench.
The Colombian, back with Monaco after dreadful loan spells with Manchester United and Chelsea, has now scored nine goals in 11 appearances this season.
Youngsters Thomas Lemar, who made his France debut earlier this week, and Gabriel Boschilia scored free-kicks to seal the win.
Monaco go clear of local rivals Nice, who visit St Etienne on Sunday, on goal difference. Paris St-Germain, champions for the past four years, sit three points off the Cote d'Azur pair.
The next game for Leonardo Jardim's Monaco is at home to Tottenham in the Champions League on Tuesday.
Match ends, Lorient 0, Monaco 3.
Second Half ends, Lorient 0, Monaco 3.
Goal!  Lorient 0, Monaco 3. Boschilia (Monaco) from a free kick with a left footed shot to the bottom left corner.
Djibril Sidibe (Monaco) wins a free kick in the attacking half.
Foul by Maxime Barthelme (Lorient).
Offside, Lorient. Steven Moreira tries a through ball, but Majeed Waris is caught offside.
Attempt missed. Majeed Waris (Lorient) right footed shot from the centre of the box is high and wide to the right. Assisted by Maxime Barthelme with a cross.
Foul by Kamil Glik (Monaco).
Majeed Waris (Lorient) wins a free kick on the left wing.
Offside, Lorient. Wesley Lautoa tries a through ball, but Majeed Waris is caught offside.
Substitution, Monaco. Boschilia replaces Bernardo Silva.
Thomas Lemar (Monaco) wins a free kick on the left wing.
Foul by Steven Moreira (Lorient).
Attempt saved. Falcao (Monaco) right footed shot from the right side of the six yard box is saved in the centre of the goal. Assisted by Bernardo Silva with a cross.
Attempt saved. Jérémie Aliadière (Lorient) right footed shot from the centre of the box is saved in the top centre of the goal. Assisted by Majeed Waris.
Bernardo Silva (Monaco) wins a free kick in the defensive half.
Foul by Cafú (Lorient).
Attempt blocked. Jérémie Aliadière (Lorient) right footed shot from the right side of the box is blocked. Assisted by Majeed Waris.
Substitution, Monaco. Guido Carrillo replaces Valère Germain.
Corner,  Monaco. Conceded by Paul Delecroix.
Substitution, Lorient. Maxime Barthelme replaces Francois Bellugou.
Falcao (Monaco) wins a free kick in the defensive half.
Foul by Zargo Toure (Lorient).
Attempt blocked. Wesley Lautoa (Lorient) header from the right side of the box is blocked. Assisted by Arnold Mvuemba with a cross.
Corner,  Lorient. Conceded by Fabinho.
Offside, Monaco. Bernardo Silva tries a through ball, but Benjamin Mendy is caught offside.
Djibril Sidibe (Monaco) wins a free kick in the defensive half.
Foul by Majeed Waris (Lorient).
Foul by Benjamin Mendy (Monaco).
Romain Philippoteaux (Lorient) wins a free kick on the right wing.
Attempt missed. Tiemoué Bakayoko (Monaco) right footed shot from outside the box is high and wide to the right.
Attempt missed. Majeed Waris (Lorient) header from the centre of the box is too high. Assisted by Arnold Mvuemba with a cross following a set piece situation.
Substitution, Lorient. Romain Philippoteaux replaces Benjamin Moukandjo.
Foul by Benjamin Mendy (Monaco).
Steven Moreira (Lorient) wins a free kick on the right wing.
Substitution, Lorient. Jérémie Aliadière replaces Sylvain Marveaux.
Goal!  Lorient 0, Monaco 2. Thomas Lemar (Monaco) from a free kick with a left footed shot to the bottom right corner.
Tiemoué Bakayoko (Monaco) wins a free kick in the attacking half.
Foul by Zargo Toure (Lorient).
Attempt blocked. Majeed Waris (Lorient) right footed shot from outside the box is blocked. Assisted by Cafú.
Radamel Falcao continued his brilliant season with a goal as Monaco beat Lorient to go top of Ligue 1.