Rudi Garcia's side were two goals to the good inside the first 10 minutes as Gervinho netted after Juan Manuel Iturbe's sixth-minute opener.
Iturbe got the ball rolling when he applied a composed finish to some good work by Gervinho and the former Arsenal misfit doubled the lead shortly after.
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Maicon made it 3-0 after 20 minutes but the goal owed a lot to a terrible mistake from goalkeeper Igor Akinfeev.
The ex-Inter Milan and Manchester City right-back's shot appeared harmless enough, but Akinfeev could not stop it squirming under his body.
Iturbe, who was enjoying a fine game, was forced to be withdrawn for Alessandro Florenzi just before the half-hour mark through injury.
Gervinho had his second of the evening on 31 minutes when he cut inside from Francesco Totti's and struck a low effort into the corner.
The home side were denied a fifth late on in the half when Akinfeev denied Miralem Pjanic with a one-handed save.
Florenzi marked his appearance from the bench with the fifth shortly after the restart before Radja Nainggolan's goal was ruled out after Gervinho had strayed offside.
Nigerian international Ahmed Musa reduced the deficit late on after racing into the box to scoop beyond Morgan De Sanctis.