Raonic, who reached the semi-finals at Wimbledon and is trying to become the first Canadian man to reach a grand slam final, had the Dominican almost under constant pressure but could only manage three breaks from 11 opportunities.
Next up for Raonic is 10th seeded Kei Nishikori of Japan who was a 6-4 6-2 6-3 winner over 23rd seed Leonardo Mayer of Argentina.
(Reporting by Steve Keating in New York. Editing by Gene Cherry)
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