She reached the semi-finals in her comeback tournament in Cincinnati three weeks ago, but looked headed for an earlier exit in an error-strewn first set against Hantuchova.
"That was definitely a nightmare," Williams said. "But I never felt that I was out of it. I just felt like I was making some errors. I just thought, `Serena, you've got to play better.'"
Williams didn't win a game until she held serve in the sixth game, in which she also fell heavily as she lunged for a forehand.
After Hantuchova wrapped up the set -- when a ball off the netcord fell her way -- Williams called for the trainer and had her left ankle taped in an injury timeout.
Hantuchova wasn't convinced Williams was hurting, particularly since she thought the American's movement improved as the match progressed.
"I don't think so, no," Hantuchova said. "But that's her call."
Williams called that remark childish.
"I obviously fell," she said. "I obviously was injured ... It was throbbing and it stung, but I just kept moving."
Williams dropped her serve to open the second set, but Hantuchova missed out on a chance to consolidate her advantage when she failed to convert two game points and was broken in the next.
Williams broke her again on her way to evening the match.
In the third, neither player faced a break point until the seventh game, when Williams converted her third opportunity when Hantuchova sailed a backhand long.
Williams fought off a break point in the next game, then broke again to take the match when Hantuchova sent a forehand over the line.
"I always had the chances to finish the point and maybe aimed it too much at the lines," Hantuchova said. "I have to give her the credit for the way she was serving, though. She hit some big serves on important points."
Hantuchova said Williams was much improved since their meeting in January.
"She's moving much better and serving really, really well," she said. "She just needs a few matches to be 100 percent back."
In the quarter-finals, Williams will meet Meghann Shaugnessy, a 6-3, 6-3 winner over Spain's Virginia Ruano Pascual.
Sharapova swept into the last eight with a with a 6-1, 6-2 win over overmatched Frenchwoman Marion Bartoli.
Safina advanced with a 6-2, 7-6 (7/2) win over American Laura Granville.
Third-seeded Zheng Jie beat Kaia Kanepi of Estonia 6-4, 6-4 on Thursday to advance to the quarter-finals of the Stockholm Open.
Also, Eva Birnerova of the Czech Republic beat doubles partner Jarmila Gajdosova of Slovakia 6-2, 6-3; Caroline Wozniacki of Denmark edged Eleni Daniilidou of Greece 7-5, 7-5; and fourth-seeded Sofia Arvidsson outlasted fellow Swede Johanna Larsson 6-2, 1-6, 6-4.
Anastasia Myskina, a finalist last year and the tournament's top-seeded player, advanced to the quarter-finals on Wednesday.
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