Murray beat Ivan Ljubicic of Croatia 6-3, 6-2 to advance to a second-round match against Italian Andreas Seppi.
The fifth seed, Gael Monfils, moved on when his opponent, Swiss qualifier Stephane Bohle, withdrew.
Sixth-seeded Spaniard David Ferrer rallied to top Austrian Jurgen Melzer 3-6, 7-6 (7-4).
Other winners included Frenchman Paul-Henri Mathieu and Grigor Dimitrov of Bulgaria.
The event's top-seeded player is world No. 1 Rafael Nadal, winner of the recent Australian Open. Nadal will open play in Rotterdam against Italian Simone Bolelli Wednesday.