Monaco have failed to win any of their first 10 home games in a Ligue 1 season for the first time in the history of the club.
Thierry Henry's side were held 1-1 at home by Patrick Vieira's Nice despite the visitors having Ihsan Sacko sent off at the end of the first half.
Benoit Badiashile Mukinayi headed a 50th-minute equaliser to cancel out the opening goal scored by Allan Saint-Maximin at Stade Louis II on Wednesday.
But Monaco could not force a winner to boost their survival hopes and even had to survive a late penalty scare against the 10-man visitors.
With 13 minutes to go, Saint-Maximin was denied by Monaco goalkeeper Diego Benaglio after a VAR review adjudged Youcef Atal to have been fouled in the box.
Henry's Monaco remain 19th in the table following the draw, which ensured they are on their worst home run in a single Ligue 1 season.
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