(MENAFN- Kora) Williams, a former world number one, won the competition in 2009 and 2010 and the wildcard entry moved into the second round by beating the Russian 6-3 6-2
Vesnina is ranked 11 places above Williams in the world rankings but was broken in the sixth game of the first set as the American showed some of the form that got her to the final of the ASB Classic in January.
Williams won 76 per cent of her first service points in the second set as Vesnina dropped three more service games to allow her opponent a comfortable progression into the second round.
The 33-year-old will now face sixth seed Angelique Kerber or Ana Ivanovic next in the WTA Premier hard court event
Italy's Roberta Vinci, a semi-finalist in the competition last year, saw her hopes of going further this time around ended by Romania's Sorana Cirstea.
The world number 27 fought back from 2-0 down in both sets to progress 6-4 6-3 and book a meeting with fourth seed Sara Errani
Like Williams, Carla Suarez Navarro was a 6-3 6-2 victor in her competition opener - the Spaniard proving too strong for Nadia Petrova of Russia.
The world number 16 won through in an hour and 20 minutes, having saved five of six break points, while Ekaterina Makarova set up a second-round clash with number one seed Serena Williams.
The Russian saw off compatriot Alisa Kleybanova 6-4 6-7 (3-7) 6-4 while Lucie Safarova had too much for American world number 18 Sloane Stephens, winning through 6-3 7-5
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