"It wasn't easy," the former world number one, who used a mix of big serves and solid groundstrokes to get by Riske, said during an on-court interview. "It was great tennis from both of us, an hour and a half of slam, bam, thank you ma'am!"
The seven-times grand slam champion has had a disappointing season so far with opening losses at Auckland, the Australian Open, Indian Wells and Miami. Sandwiched between those losses was a title triumph in the inaugural Taiwan Open.
The 35-year-old Williams, in search of her 50th WTA title, will next face Kazakhstan's Yulia Putintseva on the unique green clay courts of Charleston for a spot in the quarter-finals.
World number 10 Bencic had no answer for Vesnina, who needed just 56 minutes to secure a 6-1 6-1 triumph and passage to the third round.
Others reaching the third round were Italian fifth seed Sara Errani and American seventh seed Sloane Stephens.
Fourth seed Lucie Safarova of the Czech Republic was upset in earlier action, falling 6-3 6-3 to American wildcard Louisa Chirico, while last year's runner-up, eighth-seeded American Madison Keys, lost to German Laura Siegemund 6-7(3) 6-4 6-4.
(Reporting by Frank Pingue in Toronto; Editing by Larry Fine)
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