Epinal, who pulled off a famous shock victory over Lyon in the 2013 French Cup, frustrated Marseille for long periods on a tricky pitch but were undone by Germain's 73rd-minute strike and Morgan Sanson's late second.
The 27-year-old produced a wonderful, curling lob from the edge of the area two minutes after coming on as a substitute to end the hosts' resistance and score his 11th goal for the club since joining from Monaco in the close season.
Midfielder Sanson slotted in to complete the victory with just seconds left of injury time and secure the 10-time winners' progress into the next round.
Two Ligue 1 sides did fall to surprise defeats in the round of 32 though, as Claudio Ranieri's Nantes, sitting fifth in the top flight, were stunned 4-3 at home in a thriller by second-division side Auxerre.
Toulouse, who sacked coach Pascal Dupraz on Monday after falling into the Ligue 1 relegation zone, lost 2-0 at second-tier Bourg-en-Bresse.
Paris Saint-Germain continue their bid for a fourth straight Cup title on Wednesday at Guingamp, while Monaco host Lyon.