Australian Open champion Sharapova, who had won her first 18 matches of the season, was outplayed when it counted by the second seed in a fluctuating match lasting two hours, 19 minutes.
World number three Kuznetsova, who lost to Slovakia's Daniela Hantuchova in last year's final at Indian Wells Tennis Garden, was delighted to beat Sharapova for the first time since Miami in 2006.
"It feels great," the 22-year-old said. "I don't think Maria played like always she can play. Neither did I. But I think it was a very good, interesting third set."
Kuznetsova will meet Ivanovic in the final.
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