Baez fired more winners (49-34) but also had more double faults (7-2) in the match lasting three hours and eight minutes.
Gaston will face Argentina's Facundo Diaz Acosta, who knocked off fourth seed Pedro Martinez of Spain 6-7 (2), 6-3, 6-4 in a three-hour, 32-minute match.
Italy's Matteo Berrettini won his eighth consecutive match in beating American wild card Nicolas Moreno De Alboran 7-6 (5), 6-3 in the quarterfinals. Berrettini saved all three break points and recorded seven aces on Thursday. He improved to 9-0 in tiebreaks over the past two weeks.
He advances to the semifinals against Germany's Yannick Hanfmann, who ousted Brazil's Thiago Seyboth Wild 7-6 (2), 6-4.
Plava Laguna Croatia Open Umag
Top seed Andrey Rublev of Russia moved closer to his third title of the year with a 5-7, 6-3, 6-2 quarterfinal victory over Hungary's Fabian Marozsan in Umag, Croatia.
Rublev won earlier in 2024 in Hong Kong and Madrid and has 16 tour-level crowns. He converted six of 15 break points and fired 10 aces to zero double faults.
He moves to the semifinals against fourth-seeded Francisco Cerundolo of Argentina, a 6-4, 2-6, 7-6 (2) winner over Italy's Lorenzo Sonego.
Czech Jakub Mensik eliminated Taiwan lucky loser Chun-Hsin Tseng 6-0, 6-4 and will face second-seeded Lorenzo Musetti of Italy, a 5-7, 6-3, 6-0 winner over Dusan Lajovic of Serbia.
Atlanta Open
Juncheng Shang, a 19-year-old qualifier from China, upset top-seeded Ben Shelton 7-6 (6), 6-4 in the second round at Atlanta.
The result was a repeat of their matchup last year at the same event, when Shang also got the best of Shelton, an Atlanta native. Shang advanced to the third quarterfinal appearance of his career, all of them coming this year.
Shang faced just one break point in the match despite managing just two aces to Shelton's 13.
Third-seeded Frances Tiafoe won 84 percent of his first serve points (46 of 55) while emerging with a 6-4, 3-6, 6-3 victory over Russia's Aslan Karatsev.
Fourth-seeded Jordan Thompson of Australia won in straight sets over French lucky loser Harold Mayot 6-2, 7-5. Japan's Yoshihito Nishioka downed American Mackenze McDonald 6-3, 6-4 and next will face Tiafoe in the quarterfinals.
Fifth-seeded Alejandro Davidovich Fokina of Spain and eighth-seeded Max Purcell of Australia also advanced.
--Reuters--