A resurgent Krejcikova, who was ranked as high as second in the world last year, won two titles and 10 of her last 11 singles matches to end 2022 on a roll.
Krejcikova brought that form to Adelaide, beating 2022 finalist Alison Riske-Amritraj of the United States 6-2, 7-6 (7/3) on her seasonal debut ahead of next week's Australian Open, where she made the quarter-finals last year.
The 2021 French Open champion, now ranked 21, won the last four games of the opening set, and rebounded well to secure the match in straight sets after seeing a match point slip by a 6-2, 5-4.
Her reward is a clash next with fifth seed Daria Kasatkina.
American Anisimova, a semi-finalist at Roland Garros in 2019 and a Wimbledon quarter-finalist last season, finally got back to winning ways after a long drought, overcoming error-strewn Russian Liudmila Samsonova 7-5, 6-3.
Her progress was in stark contrast to last week's performance in Adelaide I, where she claimed only three games in a first-round defeat to world number nine Veronika Kudermetova.
The 21-year-old is looking to re-create the form that saw her come from a set down to depose defending champion Naomi Osaka in the Australian Open third round last year.
China's Zheng Qinwen set up a second-round contest with two-time Wimbledon winner Petra Kvitova via a come-from-behind 4-6, 6-4, 6-0 victory over American Shelby Rogers, while Anna Kalinskaya ousted Jelena Ostapenko.
In the men's draw, world number 35 Tommy Paul won his season-opening match 6-4, 7-5 against Australian Christopher O'Connell.
Other winners included Australian John Millman and Dutch veteran Robin Hasse.
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