Cilic, seed fourth, rallied to beat Somdev Devvarman 5-7, 6-1, 6-3. He saved just one of three break points for Devvarman but didn't face any in the second or third sets when he won 68 percent of the points on serve.
Bogomolov defeated Philipp Kohlschreiber 6-4, 3-6, 7-5 with three service breaks in the third set. He won as many points (20-20) as Kohlschreiber did in the set off Kohlschreiber's serve.
Andreas Seppi beat Igor Andreev 3-6, 6-2, 6-4 and Dusan Lajovic got by Dudi Sela 2-6, 6-2, 6-1 in the other second-round matches.
Tipsarevic goes against Starace and Bogomolov takes on Lajovic in quarterfinals action Friday. The other quarters have Cilic facing Seppi and fifth-seeded Mikhail Youzhny playing Adrian Mannarino.