Ljubicic defeated Spaniard Fernando Vicente, 6-3, 3-6, 6-4, while Ginepri beat Denmark's Kenneth Carlsen, 6-3, 6-4.
But sixth-seeded Spaniard Juan Carlos Ferrero, a former world No. 1, lost to German qualifier Mischa Zverev, 4-6, 6-2, 6-4.
Other first-round winners included German Benjamin Becker, Britain's Alex Bogdanovic, Russian Mikhail Ledovskikh and Canadian Frank Dancevic. Becker ended Andre Agassi's career earlier this month at the U.S. Open.