The seventh-seeded Croat broke for a 4-2 lead in the final set.
Ljubicic also broke Serra's serve at 4-4 in the first set, but the Frenchman dominated the second-set tiebreaker, winning five straight points to take a 5-1 lead before leveling the match at one set apiece.
Nieminen, who won the Sydney International last month, dropped serve twice to lose the opening set. The Finnish lefty saved four break points in the next set to force a tiebreaker, but Roger-Vasselin jumped out to a 4-0 lead before clinching victory.
Cipolla earned the only break of an all-Italian match in the opening game. He then erased all seven break points he faced.