The underdog saved two set points in the opener, but Murray created a third with a powerful forehand down the line and followed it up with another telling winner that clipped the left line.
A break in the second game of the second set put Murray in control, and although it was not convincing from the second seed after that, he closed the door each time Roger-Vasselin created an opening.
Murray faced two break points in the fifth game and again in the seventh, but each time he climbed out of the hole, and he sealed his progress when Roger-Vasselin chipped a backhand inches long.
Awaiting Murray in the second round is Austrian Dominic Thiem, who got the better of Finland's Jarkko Nieminen in a deciding set.
