The Scot won 6-3 6-3 in an hour and a half at the Ahoy venue where he is attempting to be champion for a second time, having beaten Rafael Nadal in the 2009 final.
It was not a classic performance from Murray, who entered the ABN AMRO World Tennis Tournament on a late wild card, but he comfortably had enough to see out the job.
Having returned from back surgery, Murray has reached the Australian Open quarter-finals and helped Great Britain through to the Davis Cup quarter-finals already this season.
On Wednesday night he had immediate chances to break serve but could not capitalise, only to make a breakthrough on the Roger-Vasselin serve in the third game, which proved to be the key moment of the set.
Murray had beaten Roger-Vasselin in each of their previous two matches, without dropping a set. Those matches came on clay in Monte Carlo last year and on hard court at the 2012 Australian Open.
On the indoor hard surface in Rotterdam it was clear who held the upper hand, with Murray’s counter-attacking negating his opponent’s threat.
Roger-Vasselin, at the age of 30, is at a career-high 35th place in the world rankings, but Wimbledon champion Murray had his number early on.
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.