Gignac, who had not spent two hours on the pitch this season after being sent on a slimming course, found the back of the net after 14 minutes.
The France international volleyed in from 20 yards after a poor clearance from the visitors' defence.
Ghana striker Jordan Ayew made it two with a fine 18-metre strike that went into the top corner in the 68th minute as Marseille won two games in a row for the first time this season.
France forward Remy put the result beyond doubt eight minutes from time, netting from close range from an Ayew deflection. He doubled his tally in the last minute, volleying home from a Mathieu Valbuena cross.
Marseille, who won the last two editions of the League Cup, have made a mediocre start to the season, having won only two of 11 Ligue 1 games as tension has grown within the club.
Ligue 1 leaders Paris Saint-Germain travel to Dijon on Wednesday.
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