Claudio Ranieri's side moved one point above Paris St Germain ahead of their clash at St Etienne in Sunday night's late game.
Mounir Obbadi and Falcao were on target in the first half for the home side, while Bafetimbi Gomis netted his second goal of the season midway through the second half for Les Gones.
The home side started well and came close to an opener just six minutes in.
James Rodriguez freed Falcao at the edge of the box and the Colombia international dribbled past a defender and fired the ball with some power towards the Lyon net before goalkeeper Anthony Lopes made a difficult block.
And Monaco's dominance paid off as they took the lead after 28 minutes through Obbadi.
Ferreira Carrasco took a free-kick from the left just outside the penalty area which Lopes managed to punch clear to the edge of the box, but the ball was not yet safe and Morocco midfielder Obbadi was well-placed to collect it and blast it into the top right of the goal.
Just eight minutes later the home side doubled their lead as Falcao netted his eighth goal of the season.
Defender Layvin Kurzawa sent up a long ball from his own half which found Falcao on the right and he ran into the box and lobbed Lopes with a close-range shot, leaving the stopper with no chance.
Lyon almost struck back just before half-time as Gomis freed Jimmy Briand and - with only goalkeeper Danijel Subasicto to beat - he shot as the keeper miraculously blocked the close-range attempt.
The second half took a while to get underway, but it was Remi Garde's visitors that started brightest and they pulled a goal back just after the hour mark.
Maxime Gonalons passed the ball down from the Lyon half to Henri Bedimo on the left, who raced to the corner and crossed the ball in for Gomis, who headed it onto the post before it went in.
Monaco were not comfortable with their one-goal lead and Falcao came close to scoring his second with a header with 10 minutes left, but Lopes pulled off a fantastic reflex save.
Then, in the dying minutes, former Lyon midfielder Jeremy Toulalan had a go at goal with a free-kick from just outside the penalty area, but his shot sailed just wide.