Despite tricky court conditions on a chilly and blustery afternoon at the California desert venue, the Russian delivered a superb display of deep, accurate groundstrokes to seal victory in just over an hour.
Second-seeded Sharapova, champion here in 2006, broke Schiavone's serve three times in each set and will next face Carla Suarez Navarro [ Images ], a 6-1, 6-1 winner over fellow Spaniard Silvia Soler Espinosa.
"I was pretty bad in the first set, but I managed to change it," Kuznetsova, a losing finalist here in 2007 and 2008, said. "So I'm pretty happy with it, but I have to change the start."
The Russian, who was sidelined by a right knee injury for six months last year after losing in the first round of Wimbledon [ Images ], did not blame her tights for her slow start but said she felt much more comfortable without them.
"Even though I tried to play in long tight pants in the first set, I cannot," the 27-year-old smiled. "I can practise in them without a problem, but when I have matches I always start to lose and I have to take them off.
"They are very tight, so they were kind of pushing my stomach and I was not so much comfortable. It was not bothering me like so much, but after I took them off I was feeling a little bit looser. It's a little bit funny."
Kuznetsova, whose world ranking has plummeted to 46th from a career-high second, will next face ninth seed Marion Bartoli [ Images ] of France [ Images ] who brushed aside South Africa's [ Images ] Chanelle Scheepers 6-3, 6-3.
Earlier, Wimbledon champion Petra Kvitova [ Images ] survived 10 double faults and an erratic second set performance to beat Olga Govortsova of Belarus 6-4, 3-6, 6-3 in the first match of the day on the second Stadium Court.
The big-serving Czech, seeded fifth in the elite WTA event at the IndianWellsTennisGarden, sealed victory after a marathon encounter lasting two hours and 21 minutes when a Govortsova forehand sailed wide.
In other matches, sixth-seeded Italian Sara Errani battled past Spaniard Lourdes Dominguez Lino 6-2, 3-6, 6-3 and 12th seed Dominika Cibulkova [ Images ] of Slovakia beat Romania's Simona Halep [ Images ] 7-5, 7-6.
Later in the day, third-seeded Agnieszka Radwanska [ Images ] of Poland was scheduled to take on American teenager Maria Sanchez.
Australian Open [ Images ] champion Victoria Azarenka [ Images ] of Belarus, who demolished Sharapova 6-2 6-3 in last year's BNP Paribas Open final, will launch her title defence against Slovakia's Daniela Hantuchova [ Images ] in the second round on Saturday.
Photograph: Danny Moloshok/Reuters