Cilic was beaten 7-6 (8), 7-6 (5) by sixth-seeded Frenchman Jo-Wilfried Tsonga, who beat the former US Open champion for only the second time in seven meetings. Tsonga had 12 aces compared with nine for Cilic, and neither dropped his serve.
Klizan was soundly beaten 6-3, 6-3 in one hour by fourth-seeded Czech Tomas Berdych, who took his three break-point chances and did not concede one on his serve. Berdych has now won all four of their matches.
Tsonga and Berdych meet in the semifinals Saturday, with Berdych holding an 8-3 lead overall.
In Friday's later quarterfinals, second-seeded Dominic Thiem of Austria fell 6-4, 7-6(3) by Pierre-Hugues Herbert of France, while No. 3 David Goffin of Belgium defeated No. 5 Grigor Dimitrov 6-4, 1-6, 6-3.