Despite tricky court conditions on a chilly and blustery afternoon at the California desert venue, the Russian world number three 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, a 6-1 6-1 winner over fellow Spaniard Silvia Soler Espinosa.
"We broke each other back and forth in the beginning of the first set, and then she had a few opportunities," Sharapova said after both players wore leggings on a surprisingly cold day at the Indian Wells Tennis Garden.
"But once I started being a little bit more aggressive I felt like I had an edge on her. She's a tough first round, that's for sure. She likes those centre court matches. She lives in those opportunities.
"She makes you hit so many balls and she has such a great slice. But, again, that's when she has time to do all that. I try to take that away from her, right from the beginning."
Schiavone, who claimed her only grand slam singles title at the 2010 French Open, has slipped to 47th in the world rankings from a career-high fourth.
In the evening match, third seed Agnieszka Radwanska of Poland wasted little time in crushing American teenager Maria Sanchez 6-2 6-1 and will next meet Romania's Sorana Cirstea, who came back to beat Spaniard Anabel Medina Garrigues 4-6 6-3 6-1.
Svetlana Kuznetsova also advanced to the third round on Friday, recovering from a poor start after discarding her long tights to upset 18th-seeded Serb Jelena Jankovic 0-6 6-2 7-5.
"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, 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 of France who brushed aside South Africa's Chanelle Scheepers 6-3 6-3.
Earlier, 2011 Wimbledon champion Petra Kvitova 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, who clinched her 10th WTA singles title in Dubai last month, will next face Ukrainian Lesia Tsurenko, who beat Kazakhstan's Yaroslava Shvedova 6-1 3-6 6-1.
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 of Slovakia beat Romania's Simona Halep 7-5 7-6.
Australian Open champion Victoria Azarenka 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 in the second round on Saturday.
BNP Paribas Open results
3-Agnieszka Radwanska (Poland) beat Maria Sanchez (U.S.) 6-2 6-1
19-Klara Zakopalova (Czech Republic) beat Shahar Peer (Israel) 6-7(2) 6-2 6-3
9-Marion Bartoli (France) beat Chanelle Scheepers (South Africa) 6-3 6-3
2-Maria Sharapova (Russia) beat Francesca Schiavone (Italy) 6-2 6-1
Svetlana Kuznetsova (Russia) beat 18-Jelena Jankovic (Serbia) 0-6 6-2 7-5
12-Dominika Cibulkova (Slovakia) beat Simona Halep (Romania) 7-5 7-6(3)
13-Maria Kirilenko (Russia) beat Christina Mchale (U.S.) 4-6 6-4 6-1
25-Carla Suarez Navarro (Spain) beat Silvia Soler Espinosa (Spain) 6-1 6-1
27-Sorana Cirstea (Romania) beat Anabel Medina Garrigues (Spain) 4-6 6-3 6-1
6-Sara Errani (Italy) beat Lourdes Dominguez Lino (Spain) 6-2 3-6 6-3
5-Petra Kvitova (Czech Republic) beat Olga Govortsova (Belarus) 6-4 3-6 6-3
Lesia Tsurenko (Ukraine) beat 31-Yaroslava Shvedova (Kazakhstan) 6-1 3-6 6-1
14-Roberta Vinci (Italy) beat Ksenia Pervak (Kazakhstan) 6-3 6-4
Johanna Larsson (Sweden) beat 26-Anastasia Pavlyuchenkova (Russia) 7-5 6-
- Sports & Recreation