Ljubicic, the No. 7 seed, got by Florent Serra 6-4, 6-7 (3-7), 6-3. He had a break in each the first and third sets for the difference in the match.
Ljubicic fired 27 aces and saw just three breaks points on the day. He dropped only five points on serve in the third set. He won only nine himself off Serra's serve but bunched enough together to record a break.
Flavio Cipolla upset No. 8-seeded Andreas Seppi 6-4, 7-6 (7-5). He fought off all seven break points he faced, including a pair in the third set. Seppi went up 5-4 in the tiebreaker and was serving but Cipolla won the last four points and advanced.
Also Monday, Edouard Roger-Vasselin defeated Jarkko Nieminen 6-2, 7-6 (7-4).
The Open 13 features four Top 10 players in No. 6-ranked Jo-Wilfried Tsonga, No. 8 Mardy Fish, ninth-ranked Janko Tipsarevic and No. 10 Juan Martin del Potro. They all have first-round byes.
Celebrity Breakups and divorces of 2014 [PHOTOS]