Cilic dropped the first set before rallying for a 4-6, 6-2, 6-3 victory at The Racquet Club of Memphis.
In other opening day matches, Rhyne Williams of the United States bested compatriot Steve Johnson 7-6, (7-4), 6-4, and Poland's Lukasz Kubot battled past American Ryan Harrison 6-4, 6-7 (4-7), 7-6 (7-2).
The second seed in Memphis is 2012 runner-up Milos Raonic of Canada, who is fresh off his third straight victory at San Jose's SAP Open.
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