Sharapova also preserved her perfect 2008 record, taking her match winning streak to 18 victories in as many appearances this year, including her Australian Open triumph in January and a title in Qatar.
"The first set I was playing like I didn't belong on that court," said Sharapova, who had to fight back from 2-5 down.
"My level was so low in that first set. She had that first set in her hands, and she didn't take it.
|"The second set was probably the best that I've played this tournament."|
"The second set was probably the best that I've played this tournament."
Hantuchova, who has won two of her three WTA Tour titles at Indian Wells, starting with her first title in 2002, had said before the match that she considered the stadium court in California her home.
"Obviously, I feel like it's my tournament, so I'm very disappointed," the Slovakian said afterwards.
"I had my chances and I didn't take them today. I feel like I lost my concentration in that first set and she took advantage of that.
"But she's playing very well, hasn't lost this season."
Kuznetsova, runner-up to Hantuchova last year, defeated Agnieszka Radwanska 6-2, 6-4, avenging her third-round loss to the Pole at the Australian Open.
"It was a good win for me after playing her in Australian Open," said Kuznetsova.
"I was more dictating my game, I was more focused and calm."
In the remaining quarter-finals, top-seeded Serbian Ana Ivanovic plays Russian Vera Zvonareva and third-seeded Serbian Jelena Jankovic meets American Lindsay Davenport.