The Scot beat the Frenchman 6-3, 6-3 at the Ahoy venue where he is bidding to win the title for a second time, having beaten Rafael Nadal in the 2009 final.
It was not a classic performance from Murray, who entered on a late wild card, but he had enough to see off the 30-year-old, who is a career-high 35th place in the world rankings. Murray missed chances to break in Roger-Vasselin's opening service game but did so two games later.
Murray had beaten his opponent without dropping a set in each of their previous two matches - on clay in Monte Carlo last year and on hard court at the 2012 Australian Open - and it was soon clear he had Roger-Vasselin's number on the indoor hard surface in Rotterdam too.
Roger-Vasselin saved two set points in the first 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 he was not convincing from that point he closed the door each time Roger-Vasselin created an opening. Murray faced two break points in the fifth game and two more in the seventh but saved them all and sealed his progress when Roger-Vasselin chipped a backhand inches long.
Awaiting Murray in the second round today is the Austrian qualifier Dominic Thiem, who got the better of Finland's Jarkko Nieminen in a deciding set. Should the Scot come through, he will face Marin Cilic in the quarter-finals. The Croat was a 6-4, 6-4 winner over the No.5 seed Jo-Wilfried Tsonga of France.
Ross Hutchins, minus his regular partner Colin Fleming, suffered a first-round doubles defeat with the Dutch 28-year-old Jesse Huta Galung. They lost 7-6 (7-1), 6-3 to the experienced French pairing of Michael Llodra and Nicolas Mahut