The top seed for the WTA International hard-court event, Lisicki recovered from an unconvincing first set, in which she double-faulted four times and got just 48 per cent of her first serves in.
Lisicki, a three-time WTA Tour winner, went 4-1 down in the first set as Niculescu took advantage to get her nose in front.
The German world number 31 also looked in deep trouble at 4-2 down in the second, but she fought back strongly to force a tie-break, where she was able to level matters.
Niculescu, ranked 60th in the world, was unable to live with her opponent in the decider as Lisicki broke twice to wrap up the set in just half an hour, sealing a last-16 clash with Grace Min.
Fourth seed Christina McHale fared worse and fell at the first hurdle, going down 6-4 5-7 6-2 to Francesca Schiavone.
The American took a 4-2 lead in the first set, but Schiavone stormed back to reel off four consecutive games to edge ahead.
McHale reversed the roles in the second, mounting an incredible comeback from 5-0 down by taking each of the next seven games to force a decider.
She could not repeat her heroics, however, as Schiavone held on to clinch the win and a second-round tie against Kimiko Date-Krumm, who saw off Johanna Larsson 6-3 6-3.
There were few shocks elsewhere, as seeds Karolina Pliskova, Zheng Jie, Jana Cepelova and Yanina Wickmayer all progressed to the last 16.
Third seed Pliskova had to do it the hard way, battling back from a set down to overcome Polona Hercog 2-6 6-4 6-3, while fifth seed Zheng had a more comfortable passage as she prevailed 6-1 7-6 (7-5) against Misa Eguchi.
Wickmayer's victory was similarly straightforward - 6-4 6-4 over Elizaveta Kulichkova - while Cepelova made short work of Chanelle Scheepers 6-2 6-1.
Australian Jarmila Gajdosova also came through in straight sets - 7-6 (7-3) 6-2 against Luksika Kumkhum - while Gajdosova's fellow qualifier Zhang Kai-Lin was also successful, 6-0 6-3 against Pauline Parmentier.
China's Zheng Saisai sealed a 7-6 (7-1) 7-5 victory over compatriot Duan Yingying, while Monica Puig defeated Patricia Mayr-Achleitner 6-1 6-1.
Elsewhere, Alison Van Uytvanck got the better of Katarzyna Piter 6-2 6-1 and Zhu Lin advanced after coming from behind to overcome Kristyna Pliskova 1-6 6-3 6-3.