The second-seeded Murray improved to 2-2 against Ljubicic, the Croatian who was runner-up in 2005 and 2007. Murray next plays Andreas Seppi.
Also, fifth-seeded Gael Monfils led Stephane Bohli 6-4, 1-0 when the Swiss player retired with a left knee injury. Sixth-seeded David Ferrer needed three sets to stop Jurgen Melzer 3-6, 7-6 (4), 7-5.
The Spaniard broke Melzer twice in the final set, including the final game.
Grigor Dimitrov, the 2008 Wimbledon and U.S. Open junior champion, defeated Tomas Berdych 4-6, 6-3, 6-4. The 17-year-old Bulgarian, ranked 478th, had 10 aces and saved nine of 10 break points against the 23rd-ranked Berdych for his first ATP Tour win.
Dimitrov will play the winner of the match between top-ranked Rafael Nadal and Simone Bolelli, who play on Wednesday.
Murray cruises past Ljubicic in Rotterdam
Valencia Always Go Out To Win - Unai Emery
