It was Monaco’s second win in three league games and saw them leapfrog Amiens and Dijon into 17th in the 20-team table.
Nicolas Pepe got the only goal after seven minutes when he slotted home after good work on the left by Jonathan Ikone.
Both sides had chances to score in an end-to-end encounter but Lille showed slightly more guile and deserved the points.
In Amiens, Monaco went ahead with a Falcao penalty two minutes before the break and the Colombian doubled the lead six minutes into added time at the end with a second from the spot.
Their miserable night was completed when Bakaye Dibassy was shown a red card seconds from the final whistle.
Elsewhere in Ligue 1, Nice drew 0-0 at home to Angers.