Kvitova, who helped Czech Republic win the Hopman Cup last weekend, needed just over an hour to beat Hantuchova, the runner-up at the Brisbane International last week.
Kvitova can pass Caroline Wozniacki for the top ranking if she wins the title this week in Sydney, a key tuneup ahead of the Australian Open.
Defending champion Li, who reached the Australian Open final last year before going to the French Open and becoming the first Chinese player to win a Grand Slam singles title, defeated Lucie Safarova of Czech Republic 6-2, 7-6 (3).
“Of course I’m feeling good,” Li said. “I won in Sydney last year and this year I’m in the semis. It’s just the beginning of the year, and I’m feeling much, much stronger.”
No. 3-ranked Victoria Azarenka beat No. 9-ranked Marion Bartoli 7-5, 6-4 and will next play either No. 1-ranked Caroline Wozniacki or Agnieszka Radwanska.
The two evening quarterfinals were delayed by a power outage at the Sydney Olympic Park Tennis Centre.
In the men’s draw, top-seeded Juan Martin del Potro defeated Lukasz Kubot 6-4, 6-2 in a second-round match, while second-seeded John Isner lost to fellow American Bobby Reynolds, 3-6, 6-4, 6-3.
Denis Istomin of Uzbekistsan also advanced with a 6-2, 6-1 win over American Ryan Sweeting.