Continuing the momentum she gained in reaching the fourth round at Wimbledon, the 22-year-old mixed powerful serves with a creative baseline attack to confuse the Slovak.
The 49th-ranked Perry was forced to qualify for the tournament, but said winning three matches in the preliminary rounds gave her confidence.
"This isn't the same feeling as reaching the second week of Wimbledon, but it's great to beat someone who has been a top 10 player," Perry told reporters. "I didn't feel much pressure."
After being spun around in the first set, Hantuchova recovered her form, overpowering Perry with crisp groundstrokes to level the match.
But Perry broke Hantuchova at the start of the third set and served huge to stay in control the rest of the way.
Keeping her slice backhand low and hammering her forehand, Perry held on to win the match when she forced Hantuchova into a forehand error.
"I made too may mistakes," Hantuchova said. "I set up the points well, but I couldn't finish them. But she played well and her serve had a lot of action on it.
Serbian Jelena Jankovic also advanced after knocking out American Lilia Osterloh 7-5, 6-3.
Playing in intense heat, the 27th-ranked Jankovic played inconsistently but wore out her opponent at key moments.
"I wasn't happy with the way I played, I made a lot of errors and I wasn't serving well," Jankovic said. "But I was able to win in two sets and not stay too long in the heat."
Jankovic, who upset defending champion Venus Williams at Wimbledon, will face top seed Kim Clijsters in the second round.
"I need to improve my serve because the way I'm serving right now is not good," Jankovic said. "I need to cut down on my unforced errors and play aggressive."
Japan's Ai Sugiyama advanced with a 6-3, 6-4 win over Czech Kveta Peschke, while Australian Samantha Stosur destroyed Olga Savchuk of the Ukraine 6-1, 6-3.
Russian 18-year-old Vasilisa Bardina upset India's Sania Mirza 6-3, 6-2 and faces fourth seed Ana-Lena Groenefeld of Germany in the next round.
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