The visitors, managed by former title-winning Lille boss Christophe Galtier had less ball possession. But overall, they deserved their win after registering seven shots on target against the two shots registered by their hosts.
The match began brightly as Jocelyn Gourvennec’s men fell behind in the first minute of the game, with Denmark’s Euro 2020 hero, Dolberg, finding the net from close range.
Three minutes later, Dane was involved again. He put Lille defender Zeki Celik under pressure to create space for Gouri, who set up Boudaoui to score past Lille’s new goalie Leo Jardim.
Despite enjoying the greater share of the ball, the hosts could not trouble their visitors, and they fell further behind just before halftime.
This time Amine Gouiri was the goal scorer as he stepped up to score from the penalty spot following a handball by Benjamin André in the six-yard box.
After the break, the visitors added their fourth of the evening with Kasper Dolberg, the scorer from a corner kick.
The result ensures that Nice, who play Marseille in their next, stay on top of the table although temporarily. Defending champions Lille, who face St-Etienne next weekend, sit in 16th place after taking just one point from their first two games.
Lillie have not conceded a huge loss like this since 2017.