The hard-court tournament serves as a warmup event for next week's U.S. Open.
In other second-round matches, No. 3 seed Roberta Vinci of Italy beat Polona Hercog of Slovenia 6-2, 6-3; No. 6 seed Peng Shuai of China defeated Pauline Parmentier of France 6-4, 6-2; Aleksandra Wozniak of Canada ousted Eugenie Bouchard of Canada 6-2, 6-2 and Bojana Jovanoski of Serbia topped Mirjana Lucico of Croatia 7-6 (5), 6-2.
Wozniak will play Dellacqua on Wednesday.