Shvedova, the tournament's top seed, breezed by Maria Elena Camerin 6-1, 6-1 in her opening draw of the hard-court tournament. Shvedova lost just 11 points on serve and saved the only break-point situation she faced in the win.
She also posted breaks of Camerin's serve five times in seven games.
Third-seeded Ioana Raluca Olaru dropped a tough 7-5, 7-5 decision to Ekaterina Bychkova, who suffered just one break of serve in the match.
Sixth-seeded Monica Niculescu blitzed Corina Dentoni 6-3, 6-0 and No. 7-seeded Patricia Mayr claimed a 7-5, 6-4 win over Ekaterina Dzehalevich in their first-round matches.
Local favorites Akgul Amanmuradova, who topped Ksenia Lykina 6-1, 4-6, 6-3, and Nigina Abduraimova, who defeated Lesya Tsurenko 6-3, 6-2, also advanced to the second round.
Other winners Tuesday were: Ekaterina Ivanova, Vesna Manasieva, Evgeniya Rodina, Alexandra Panova, Kathrin Woerle and Darya Kustova,
The tournament continues through Sunday when the champion will earn $37,000.
Swim Week Miami Beach 2014 [PHOTOS]