The 33-year-old Baghdatis next faces Radu Albot of Romania, who labored into the last eight by beating Ernests Gulbis of Latvia 7-6 (5), 4-6, 6-4. Earlier, third-seeded Denis Shapovalov of Canada used his strong serve to beat Marcel Granollers 6-4, 7-6 (1).
The 19-year-old wild-card entry did not face break point and won 30 of his 33 first-serve points against the Spanish veteran. Shapovalov was one of only two players to take a set from Djokovic at last month's Australian Open, but he has yet to win a career title on the ATP Tour.
He next faces seventh-seeded Frenchman Pierre-Hugues Herbert, who rallied to a 4-6, 6-4, 6-2 win against Ilya Ivashka of Belarus.
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