Galtier led Lille to the title last season, as Les Dogues edged out Paris Saint-Germain.
While PSG has added more remarkable talent to its already world class squad, with the arrivals of Sergio Ramos, Georginio Wijnaldum, Achraf Hakimi and Gianluigi Donnarumma – topped off by the signing of Lionel Messi – Lille has had to contend with the loss of its coach, who left the club to join Nice in the off-season.
Galtier and Lille hardly parted on good terms internally, despite the 54-year-old delivering the club's first title in a decade.
There have also been rumblings of discontent at Nice, with tensions reportedly appearing between Galtier and sporting director Julien Fournier as they aim to bolster the squad.
A disappointing 0-0 home draw to Reims started Galtier's tenure, but Nice put that well behind it with a thrilling showing against the champion on Sunday (AEST).
Kasper Dolberg got the ball rolling inside 57 seconds after Amine Gouiri had caused havoc in the Lille defence – that was the earliest Ligue 1 goal scored by the club since April 2013 (32 seconds).
Gouiri then teed up Hichem Boudaoui for a fierce effort four minutes later to make it 2-0. The former ensured Nice was 3-0 up at the break for the first time since October 2014 as he converted a penalty on the stroke of half-time.
Dolberg completed the scoring just past the hour, with Gouiri denied a second of his own soon after due to offside.
It was the first time since September 2017 that Lille had conceded four goals in a single home league match and Galtier basked in the achievement.
"It's a great victory," he said.
"We knew that we were going to face a side that has been in place for a certain period of time and that our first match against Reims wasn't good enough.
"Against Reims, we were missing a lot of things. The players did well [against Lille]. It's their victory because they have come a long way."
Asked what it meant to defeat his old side in such an emphatic manner, Galtier replied: "I haven't had the time to reflect on that yet. It's always good to keep your feet firmly on the ground and to remain vigilant after this kind of victory, which seems easy when you look at the score.
"But it's a victory that required a lot of commitment and energy. We can't ease our feet off the pedals throughout the week or allow what we are demanding in training to drop off."
The defeat means Lille is still waiting for its first win of the season. It is the third time it has failed to triumph in either of its opening two matches of a campaign in which it has been defending champion.