Cilic was beaten 7-6 (8), 7-6 (5) by sixth-seeded Frenchman Jo-Wilfried Tsonga, who defeated the former U.S. Open champion for only the second time in seven meetings. Tsonga had 12 aces compared to nine for Cilic and neither dropped their 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 of their four matches.
Tsonga and Berdych meet in the semifinals Saturday, with Berdych holding an 8-3 lead overall.
"Tomas is very consistent and covers the court well," said Tsonga, who is chasing his 400th career match win. "I will try to dictate from the very beginning."
Also, third-seeded David Goffin of Belgium finally got the better of Grigor Dimitrov, beating the beat fifth-seeded Bulgarian 6-4, 1-6, 6-3 in a match where both players conceded 13 break points and got broken twice.
Goffin had lost their previous three matches, including last weekend's Sofia Open final in Bulgaria and a straight sets loss in the Australian Open quarterfinals last month.
Goffin next faces Frenchman Pierre-Hugues Herbert, a doubles specialist ranked 109 who upset second-seeded Dominic Thiem of Austria 6-4, 7-6 (3) in their first ever meeting. Herbert had eight aces and secured the only break of the match, while saving all three break points he faced.
Herbert and Goffin play each other for the first time.