Remy, who scored France's opener in a 2-0 win against Romania in a Euro 2012 qualifier last Saturday, netted from close range after being set up by fellow France striker Andre-Pierre Gignac in the 27th minute.
Three days before they host Zilina in the Champions League, Marseille failed to impress but they jumped to fourth overall. They are three points adrift of Stade Rennes, who travel to strugglers RC Lens on Sunday.
"It was not our best match but the most important thing is that we won it," coach Didier Deschamps was quoted as saying on Marseille's website.
Marseille were level on points with Paris Saint-Germain, who moved up to third thanks to a 2-0 victory at Toulouse.
Defender Mamadou Sakho put the visitors ahead with a powerful shot from just inside the box and Turkey striker Mevult Erding made it 2-0 in the second half after being set up by a Ludovic Giuly defence-splitting pass.
Girondins Bordeaux, the 2009 champions, moved up to seventh, after a 19th-minute goal by Anthony Modeste gave them a 1-0 win at AJ Auxerre.
France captain Alou Diarra was sent off in the 70th minute for shoving referee Wilfried Bien after being shown a yellow card.
Diarra apologised but it was too late and Bordeaux held on for the points.
"We are solid defensively but we need to do much better offensively," Bordeaux coach Jean Tigana told a news conference.
"Alou (Diarra) is a good guy, he apologised to everyone for what he did," he added.
Bottom club Arles-Avignon picked up their first point of the season in a goalless away draw at Brest.
