Jeremy Chardy of France beat the seventh-seeded Ancic 6-4, 3-6, 6-4, while Kazakh qualifier Mikhail Kukushkin saved two match points before ousting the fifth-seeded Cilic 7-6 (4), 4-6, 7-6 (6).
After trading breaks early in the third set, the 23rd-ranked Cilic had two match points at 6-4 in the tiebreaker. But the 158th-ranked Kukushkin won four consecutive points to score his first career victory over a seeded player in an ATP event.
Cilic had 19 aces in the match to Kukushkin's 10.
The 74th-ranked Chardy capitalized on Ancic's double fault in the fifth game to take the first set. Ancic, ranked 36th, leveled the match with a break in the eighth game of the second set and had an early break in the decider to go 3-1 up.
Chardy broke back to 3-3 and saved two break points in the ninth game before closing with the second match point on Ancic's serve.
Two-time former champion Mikhail Youzhny of Russia, seeded fourth, advanced by defeating Ivan Navarro of Spain 6-2, 6-1.
Youzhny, who won the tournament in 2002 and 2004, won five consecutive games and had two breaks in the second set.
Also, Russian wild card Michail Elgin beat Filippo Volandri of Italy 6-4, 6-4.
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