Dolgopolov had four match points -- two in the tiebreak -- before Roger-Vasselin came back to win.
Asked what made the difference in the match, Roger-Vasselin, ranked No. 106 in the world, said, "Maybe luck. He missed one or two easy shots on the match point but otherwise it was very close."
The French qualifier will meet Ivo Karlovi of Croatia in Friday's quarterfinals. Karlovi defeated Alexander Bogomolov Jr. of Russia 7-6 (13-11), 6-4 in their second round match.
Jerzy Janowicz of Poland reached the quarterfinals by upsetting seventh seed Carlos Berlocq.
Janowicz, ranked 74th in the world, downed Berlocq 6-3, 6-4 in a second round match and will play No. 4 seed Thomaz Bellucci in the quarters. Bellucci advanced by defeating Flavio Cipolla, 6-4, 6-1.
Moscow is the third straight tournament in which Janowicz has reached the quarterfinals.
No. 2 seed Andres Seppi beat Igor Sijsling 7-5, 6-2 and plays eighth-seeded Tatsuma Ito Friday and Lukas Rosol will take on Malek Jaziri in another quarterfinal match.