The world number 59 broke the Italian to take the first set and broke again to move ahead 3-1 in the second before recording one final break to close out the contest and collect her first win in four meetings with the 2010 French Open champion.
Schiavone, the first Italian woman to win a Grand Slam, has been in miserable form losing seven consecutive first-round matches before ending the barren stretch last week at the BNP Paribas Open in Indian Wells.
Shvedova, whose only career WTA Tour win came seven years ago in Bangalore, has lost all three meetings with Williams but did push the six-times Miami champion to three sets during a round of 16 meeting at the 2012 Wimbledon.
It was the second match win of the season for the 58th ranked Puerto Rican.
The tournament began on a down note for the home contingent with American Bethanie Mattek-Sands falling 6-3 3-6 6-3 to Ukraine's Elina Svitolina.
Sony Open results
Anna Karolina Schmiedlova (Slovakia) beat Indy de Vroome (Netherlands) 7-5 5-7 6-2
Alisa Kleybanova (Russia) beat Iveta Melzer (Czech Republic) 7-6(3) 6-1
Chanelle Scheepers (South Africa) beat Silvia Soler Espinosa (Spain) 6-3 6-0
Varvara Lepchenko (U.S.) beat Yanina Wickmayer (Belgium) 7-5 6-1
Monica Puig (Puerto Rico) beat Magdalena Rybarikova (Slovakia) 6-1 7-6(7)
Casey Dellacqua (Australia) beat Stefanie Voegele (Switzerland) 6-3 6-2
Romina Oprandi (Switzerland) beat Bojana Jovanovski (Serbia) 6-2 6-4
Yaroslava Shvedova (Kazakhstan) beat Francesca Schiavone (Italy) 6-4 6-2
Kurumi Nara (Japan) beat Annika Beck (Germany) 7-6(2) 6-4
Caroline Garcia (France) beat Aleksandra Wozniak (Canada) 6-3 7-5
Elina Svitolina (Ukraine) beat Bethanie Mattek-Sands (U.S.) 6-3 3-6 6-3
Tsvetana Pironkova (Bulgaria) beat Galina Voskoboeva (Kazakhstan) 6-2 7-5
- Sports & Recreation