Marseille hit twice on the break and defended diligently to see off a largely ineffective Paris Saint-Germain side in the Coupe de France last 16 on Wednesday night.
Lionel Messi was nowhere to be seen as the visitors suffered without the injured Kylian Mbappe, and crashed out of the cup thanks to a 2-1 loss at Stade Velodrome.
The home side were on the front foot for most of the opening 30 minutes, forcing Gianluigi Donnarumma into a series of saves. And they were eventually rewarded, with Alexis Sanchez sending Donnraumma the wrong way from the penalty spot after a clumsy foul from Sergio Ramos.
Ramos redeemed himself on the stroke of half-time, nodding a Neymar corner into the ne, but the hosts retook the lead shortly after the break, with Ruslan Malinovskyi smashing the ball past a sprawling Donnarumma after a passage of poor PSG defending.
Galtier's side pushed for an equaliser for the remainder of proceedings, but Marseille retreated deep into their own half. And without the threat of Mbappe's pace and trickery, PSG failed to create much.
The loss marked Galtier's first major setback at the helm. The first-year manager has met every expectation so far, leading PSG into the Champions League knockout stages and establishing a convincing lead atop Ligue 1.
But his side, with their financial power and raw quality, should be winning every trophy available to them.