Hantuchova, the 2002 champion at Indian Wells, needed almost three hours to get the better of a stubborn Peer, with the pair engaging in several punishing baseline rallies.
The 23 year-old Hantuchova served for the match at 5-4 in the third set, and came back from 3-5 down in the ensuing tie-break to finish on top after her teenage opponent crumbled under some late unforced errors.
"I think we both started to feel it in the middle of the third set because we had long rallies, and also the match yesterday with Martina was not easy," Hantuchova said, alluding to her second successive defeat of the former world number one.
"I was running from one side to another, but it's a great feeling to be tired like that."
Hantuchova, who has ended the year ranked in the top 20 on four separate occasions, believes she has matured enough to challenge the top players.
"I'm understanding much better, if something goes wrong, it's part of the game, and it's okay, not to be perfect all the time," she said.
"And just to try to figure out how to turn things around in my way and always try to stay positive."
A little loose
Meanwhile, Li was impressive against the agile Zvonareva, hitting some valuable winners on the big points and tiring out her Russian opponent, who had upset world number one Maria Sharapova in the previous round.
Li, who was trailing 5-1 in the second set, won six straight games as Zvonareva lost depth on her shots and was pushed deeper on the court.
"After winning the first set, I was a little bit loose," the 12th seeded Li said.
"At 5-1, I noticed the balls were coming back slower."
In the bottom half of the women's draw, sixth seed Nicole Vaidisova of the Czech Republic will play second-seeded Russian Kuznetsova in one quarter-final, while in the other, 33rd seed Sybille Bammer takes on 13th seed Tatiana Golovin.