Bulgarian striker Berbatov casually lobbed David Ospina from the edge of the box in the fifth minute to lift his side on to 72 points with four games left.
Claudio Ranieri's side trail leaders PSG by seven points with the French champions playing their game in hand against Evian Thonon Gaillard on Wednesday.
Had Monaco lost on Sunday, PSG could have wrapped up the title on Wednesday with a victory against lowly Evian.
Assuming PSG beat Evian, the earliest they can wrap up their second successive Ligue 1 title is next weekend if the Paris club beat Sochaux away or pick up as many points as Monaco.
Monaco, who lead third-placed Lille by nine points before the Northerners travel to Olympique Marseille later on Sunday, were quickly in front thanks to Berbatov's cool finish.
They came very close to doubling the tally in the 12th minute when Valere Germain's strike smashed the post.
Nice's best chance came in the 21st minute when Valentin Eysseric's shot was tipped away by Danijel Subasic.
The win eased the pressure on Monaco coach Ranieri after his team were knocked out in the French Cup semi-final by En Avant Guingamp on Wednesday.
AC Ajaccio were relegated to Ligue 2 after they suffered a 2-1 defeat at fellow Corsicans Bastia.
The result left them on 20 points with four games left, 15 points behind 17th-placed En Avant Guingamp.
It was a goal scoring feast elsewhere as 10-man Montpellier let a three-goal lead slip in a 4-4 draw at Lorient, conceding three goals in the final trhee minutes.
Girondins Bordeaux still have an outside chance of making it to the Europa League after a 5-1 win over Guingamp while Valenciennes's hopes of staying in the top flight suffered a blow in a 6-2 home loss to Nantes.
In the day's late kick-off, Lille edge towards a Champions League spot with a 0-0 draw at Marseille.
- Sports & Recreation
- Evian Thonon Gaillard