Tsitsipas saved two match points in a 3-6, 7-6 (11), 6-4 victory over second-seeded defending champion Alexander Zverev, and the top-seeded Nadal beat sixth-seed Marin Cilic 2-6, 6-4, 6-4.
Zverev, the German star coming off a victory last week in Washington, double-faulted on match point to send Tsitsipas to his first ATP World Tour Masters 1000 semifinal.
The 19-year-old Tsitsipas beat seventh-seeded Dominic Thiem and ninth-seeded Novak Djokovic to reach the quarterfinals. He's the youngest player to beat three top-10 players in one tournament since Rafael Nadal - who also was 19 - in 2006 at Monte Carlo.
Tsitsipas will face fourth-seeded Kevin Anderson in the semifinals, trying to become the youngest to beat four straight top-10 players in an event since the ATP World Tour was established in 1990. Anderson beat fifth-seeded Grigor Dimitrov 6-2, 6-2.
The top-seeded Nadal will play Karen Khachanov, a 6-3, 6-1 winner over Robin Haase.
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