Isner, a six-time winner of the event, saved four match points in the next-to-last game before Brooksby closed out his victory.
Up next for Brooksby is a showdown with another U.S. player, Frances Tiafoe. The fourth-seeded Tiafoe got past eighth-seeded American Brandon Nakashima 6-4, 6-2.
Third-seeded Australian Alex de Minaur posted six aces while rallying for a 4-6, 6-3, 6-0 victory over France's Adrian Mannarino to reach the semifinals.
The 23-year-old de Minaur, who won the event in 2019, will face Ilya Ivashka of Belarus in the semis. Ivashka, 28, upset fifth-seeded Tommy Paul 6-2, 3-6, 6-1.
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Croatia Open Umag
Top-seeded Carlos Alcaraz won 81.3 percent of his first-serve points while cruising to a 6-0, 6-4 victory over Argentina's Facundo Bagnis to reach the semifinals in Umag, Croatia.
The Spanish teen next faces Italian qualifier Giulio Zeppieri, who knocked off Spain's Bernabe Zapata Miralles 7-5, 6-4. Zeppieri had a 6-5 edge in aces.
Second-seeded Italian Jannik Sinner beat Spain's Roberto Carballes Baena 6-4, 7-6 (5) to reach the semis. Sinner will face Franco Agamenone, who defeated fellow Italian Marco Cecchinato 6-2, 6-1.
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Generali Open
Third-seeded Roberto Bautista Agut won 70.2 percent of his first-serve points en route to a 6-3, 7-6 (3) victory over fellow Spaniard Albert Ramos-Vinolas to reach the final at Kitzbuhel, Austria.
Bautista Agut led 5-2 in the second set before the fifth-seeded Ramos-Vinolas made a charge and won the next four games. But Bautista Agut rolled through the next game and won the tiebreaker to advance to play either Austrian wild card Filip Misolic or Germany's Yannick Hamfmann.
Misolic led Hanfmann 6-2, 2-6, 6-6 (1-0) when play was stopped due to heavy rain, and the match will resume Saturday. Misolic beat Serbia's Dusan Lajovic 2-6, 7-6 (5), 6-3 earlier Friday after their Thursday quarterfinal match was postponed a day due to rain.
