Lisicki and Kuznetsova through
Lisicki endured a 90-minute delay for heavy rain that halted her momentum before she scratched out a 7-6 3-6 6-3 victory over fellow German Mona Barthel.
Kuznetsova was forced off for 35 minutes with the score 30-30 while she was leading 5-1 in the second set against American teenager Christina McHale.
When the pair returned they warmed up for nine minutes before some stoic defence by McHale, who saved three match points. They played for another four minutes with the twice Grand Slam winner sealing the 6-1 6-1 victory when McHale's forehand floated wide.
"It was strange, because it was a few points away and the game could have gone either way and it was difficult to maintain concentration but I think it worked out pretty good for me," Kuznetsova said.
"I was playing well. I did have some unforced errors but I completed my game plan and I'm happy with my performance," she added after her demolition of the highly-rated American, who had beaten the former world number two twice in the last year.
Lisicki also suffered a weather delay earlier on Wednesday. The 22-year-old had broken Barthel to take a 6-5 lead in the first set and seemed to be getting on top before rain swept across central Auckland and forced the players off.
They returned about 90 minutes later but the momentum the world number 15 had gathered before the rain dissipated and she was broken to force the set into a tie-break, which she won 7-3.
Barthel rallied to overcome a 0-2 deficit in the second set as neither player seemed to able to hold serve, and Lisicki's swinging second serve on set point down failed to find the centre line, forcing a decider.
Lisicki raced to a 3-0 lead in the final set and sealed victory on her second match point when Barthel's cross-court backhand smacked into the net.
"I improved from my last match, which I knew I had to," Lisicki said. "I still didn't play consistently enough to win in two sets but the most important thing when you don't play your best tennis is still to find a way to win."
Second seed Peng Shuai lost 6-4 6-3 to Lucie Hradecka, fifth seed Julia Goerges went down 6-2 6-3 to Angelique Kerber, sixth seed Roberta Vinci was beaten 6-3 6-4 by Elena Vesnina and eighth seed Monica Niculescu was trounced 6-0 6-2 by Zheng Jie before seventh seed and 2010 champion Yanina Wickmayer lost to Italy's Sara Errani 4-6 6-1 6-1 in the night session.