Murray, who reached the high-water mark of his career last year by winning both the Olympic gold medal and the U.S. Open, ousted Cilic 6-4, 6-3. He will take on Richard Gasquet in the semifinals after Gasquet surprised fourth-seeded Tomas Berdych 6-3, 6-3.
Murray earned a semifinal berth in this tournament for the fourth time, recording six breaks of serve while defeating Cilic for the eighth time in nine meetings. Cilic committed 37 unforced errors.
Murray lost in last year's final to world No. 1 Novak Djokovic, but Djokovic was eliminated from this year's event in the fourth round by Haas.
Gasquet, trying for his first championship in a Masters Series tournament, converted three of his four break chances. Gasquet now owns a 5-3 career record against Berdych, although Berdych had defeated him two weeks ago at the Masters event in Indian Wells.
Murray and Gasquet have met seven times with Murray having won four of those confrontations. Their last match came in the round of 16 at last year's French Open, a meeting won by Murray in four sets.
Ferrer has captured his only two previous matches against Haas, but they have not faced each other in five years.