Murray, seeded second in Rotterdam, was broken in his first service game and again in the fifth game of the second set as he lost 6-3 6-4 in 71 minutes.
It was Cilic's second win over Murray in 11 FedEx ATP meetings. Cilic, who last beat Murray at the 2009 US Open, has now won 16 straight sets on the ATP World Tour. Last week, he lifted his fourth PBZ Zagreb Indoors title when he beat Tommy Haas in the final.