Bulgarian striker Berbatov casually lobed David Ospina from the edge of the box in the fifth minute to put his side on 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.
Sunday’s result means that provided 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 was knocked out in the French Cup semi-final by En Avant Guingamp on Wednesday.