There was almost nothing to separate the two players, but Strycova raised her game in the third set and played some delightful tennis to seal the match.
Strycova will face under-rated American Lauren Davis in the quarter finals, and will combine with Safarova later tonight for a doubles match, where they are top seeds.
Kiwi wildcard Jade Lewis fell at the first hurdle against Venus Williams, but not without a sterling effort.
Lewis, who was playing her first WTA match, pushed the American legend to the limit in the first set, before eventually succumbing 7-6 (2) 6-2 in 88 minutes.
Lewis will rue some chances that got away, especially when she had two chances to serve for the first set and also held a set point, but overall this match was a lot closer than most pundits had predicted.
Given there was a rankings disparity of more than 1000 places between the duo, there were some fears that the 18-year-old Kiwi could be blown off the court.
But Lewis, who is the niece of 1983 Wimbledon finalist Chris, more than held her own in a messy first set, which featured six breaks of serve.
After the match restarted at 2-2, neither player could hold serve for the first three games on Wednesday, before Lewis eventually held to take a 5-3 lead.
Lewis had a set point at 5-4, but couldn't take advantage, holding her head in her hands as Williams broke back.
Lewis had another chance at 6-5, when a series of Williams double faults opened the door for the Kiwi, but couldn't take it.
That was her last chance.
Williams came to life in the tie-breaker, while Lewis came up with several loose shots.
The second set was more of a procession. While Lewis never stopped trying and came up with some beautiful winners, the emotional energy of the first set seemed to take its toll.
A pep talk from coach Simon Rea raised her spirits for a while, but Williams raced to a 5-0 lead as Lewis lost her range.
Lewis fought to the end, saving one match point, but Williams eventually wrapped up a hard-fought win.
"I'm thankful to get through," said Williams afterwards. "She's very talented.
"She has a fire inside her, I love to see that in a young player.
"I remember when I was her age. It was a long time ago, but I still remember.
"The first match of the year is never perfect, but I'm happy to be into the next round and playing another teenager. I'm just feeling old."
Meanwhile, on the outside courts, Crotian eight seed Ana Konjuh finally put away Belgian Kirsten Flipkens 6-4 3-6 6-3 in another match that began yesterday and went for more than two hours.
Konjuh is scheduled for a centrecourt showdown with former ASB Classic champion Yanina Wickmayer later this afternoon, as organisers scramble to make up lost time with the draw.
Briton Naomi Broady has overcome Danka Kovinic of Montenegro 7-6 6-3 and will meet German Julia Goerges later today.
Goerges, the beaten 2016 finalist progressed over sixth-seeded Rusian Anastaria Pavlyuchenko 6-3 6-4 in 1h 26min.
A crowd favourite in seven previous visits to the Auckland tournament, she reached the semi-finals in 2011 and losing to American Sloane Stephens last year.
Today's results:
Singles
Second Round
Barbora Strycova (4), Czech Republic, def. Lucie Safarova, Czech Republic, 7-5, 3-6, 7-6 (4).
Lauren Davis, United States, def. Kurumi Nara, Japan, 6-3, 6-3.
Madison Brengle, United States, def. Serena Williams (1), United States, 6-4, 6-7 (3), 6-4.
Jelena Ostapenko, Latvia, def. Mirjana Lucic-Baroni, Croatia, 6-2, 7-6 (3).
Naomi Osaka, Japan, def. Venus Williams (2), United States, walkover.
Doubles
First Round
Demi Schuurs, Netherlands, and Renata Voracova, Czech Republic, def. Tatjana Maria, Germany, and Nicole Melichar, United States, 4-6, 6-4, 10-7.
Gabriela Dabrowski, Canada, and Yang Zhaoxuan (4), China, def. Jocelyn Rae and Anna Smith, Britain, 7-5, 6-2.
Maria Irigoyen, Argentina, and Ipek Soylu, Turkey, def. Miyu Kato, Japan, and Arina Rodionova, Australia, 6-2, 7-6 (2).
Marina Erakovic, New Zealand, and Laura Robson, Britain, def. Alicja Rosolska, Poland, and Taylor Townsend, United States, 6-1, 7-5.
MORE TO COME
