Ferrer, seeded fourth, fell behind Ivan Ljubicic before collecting a 3-6, 6-2, 6-1 win. Ferrer didn't face a break point after the first set.
The fifth-seeded Cilic, looking for his third tournament win this year, had a tougher time in his 2-6, 7-6 (7-3), 6-4 victory over Janko Tipsarevic. Cilic broke Tipsarevic's serve just once in the match -- that coming in the third set -- and won just three more total points.
Second-seeded Andy Murray also dropped a first set before advancing when Sergiy Stakhovsky retired in the third set due to an ankle injury. Murray was credited with a 6-7 (3-7), 6-3, 5-3 victory.
Seventh-seeded Ivo Karlovic was ousted in three sets by Marco Chiudinelli, 7-6 (7-4), 4-6 (7-6 (9-7).
Also winning Monday were Teimuraz Gabashvili and Fabrice Santoro.
Top-seeded Novak Djokovic has his first match of the tournament Tuesday.
The Dubai winner will take home $383,000.