But Nadal, 30, won four successive games to clinch the opening set and the 14-times grand slam winner broke twice in the second to see off 2012 Brisbane finalist Dolgopolov in one hour 15 minutes. He will next play Germany's Mischa Zverev.
In the women's draw, Spanish fourth seed Garbine Muguruza saved a match point before beating 19-year-old Russian Daria Kasatkina 7-5 3-6 7-6(7) to reach the last eight where she will face Destanee Aiava or twice grand slam champion Svetlana Kuznetsova.
Australian 16-year-old Aiava upset American Bethanie Mattek-Sands 2-6 6-3 6-4 to become the first player born after the year 2000 to win a WTA main draw match.
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World number six Karolina Pliskova crushed American qualifier Asia Muhammad 6-1 6-4 to set up a quarter-final meeting with eighth seed Roberta Vinci or Japan's Misaki Doi.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
