Claudio Ranieri's side moved above Lille in the table after Emmanuel Riviere struck his eighth goal of the season.
The striker pounced with 15 minutes remaining to ensure Monaco capitalised on the sending off of Jean-Baptiste Pierazzi and claimed a fourth straight win.
Vincent Enyeama's bid to break the record for consecutive minutes without conceding in Ligue 1 came to an end as Lille suffered a first defeat in 12, losing 1-0 at Bordeaux
That record stood at 1,176 minutes, but the Nigerian goalkeeper's run came to a halt at 1,062 when Landry N'Guemo scored with the aid of a deflection in the first half.
Even the dismissal of Bordeaux defender Maxime Poundje after 58 minutes was not enough to bring Lille back into the game.
Lyon got back to winning ways with a comfortable 3-1 victory over Bastia.
Florian Raspentino gave Bastia the lead in the 34th minute, but second-half goals from Alexandre Lacazette, Yassine Benzia and Bafetimbi Gomis earned all three points for Lyon.
Elsewhere on Sunday, Montpellier's winless run was stretched to eight league games with a 1-1 draw against Toulouse.
Souleymane Camara was on target for the 2011-12 champions, while Abel Aguilar levelled after both sides had been reduced to 10 men in the second half.