The eighth-seeded Ljubicic, who won the title in 2005, hit 21 aces to set up a match with Janko Tipsarevic of Serbia.
Tipsarevic beat 2003 winner Arnaud Clement of France 6-4, 6-4.
The Serbian broke Clement once in each set and relied on a solid serve, winning 80 percent of his service points without allowing any break opportunities.
Richard Gasquet of France saved two break points at 5-5 in the third set to outlast Michael Berrer of Germany 6-3, 2-6, 7-6 (5).
The Frenchman is trying to rediscover his form after the International Tennis Federation banned him for two and a half months for testing positive for cocaine at a tournament in Miami in March. Gasquet said he inadvertently ingested the drug by kissing a woman in a nightclub.
Nicknamed in his youth the Mozart of tennis by the French media because he was the most talented player of his generation, Gasquet reached a career-high No. 7 ranking in 2007. He was a finalist here in 2004, but Tuesday's win was only his second since his return to the tour a month ago.
Gasquet will next face Christophe Rochus of Belgium, who edged fifth-seeded Fabrice Santoro of France 0-6, 6-4, 7-6 (3).
Sixth-seeded Benjamin Becker of Germany was also ousted, as Evgeny Korolev of Russia converted all of his four break chances to win 6-2, 6-3.
Denis Istomin of Uzbekistan defeated Andrey Golubev of Kazakhstan 6-2, 6-4, Marc Gicquel of France cruised past Roman Valent of Switzerland 6-3, 6-1, and qualifier Thierry Ascione upset Adrian Mannarino 7-6 (5), 6-4 in an all-French matchup.
Mannarino, a semifinalist last year, has been suffering for three weeks from a knee inflammation and will no longer play this year to let his injury heal.
Silva leaves exit door openITF appeals doping ruling that cleared Gasquet
