Kuznetsova, a former French and U.S. Open winner, was playing her first match since straining her groin in November. The third seed hit eight aces to beat Riske in 75 minutes.
"I missed playing for one and a half months and obviously I was a little bit slow, but I was calm and in the end it was a good game," Kuznetsova said.
Kuznetsova's next opponent, American Christina McHale, has beaten her in their two previous matches.
In other matches, second-seeded Peng Shuai of China dropped a set before beating French qualifier Aravane Rezai 6-4, 3-6, 6-4, while defending champion Greta Arn of Hungary was beaten 7-5, 3-6, 6-4 by fifth-seeded German Julia Goerges.
Peng, China's No. 2 player, struggled with early season rustiness before overcoming Rezai in two hours.
"It's been a long time since I last played and it was my first match of the year so I was a little nervous," she said. "I was tired and so slow and it was hard to get into the match because she hit the ball so well. It was like boom, boom, boom."
Goerges won her match despite feeling ill and taking a long medical break at the start of the third set, during which her pulse and blood pressure were taken.
After losing a first set in which she converted only one of nine break-point chances, Arn took charge in the second, saving all three break points she faced and converting two of seven on her own serve.
Goerges signaled to her coach several times during the third set that she was tired and lacking energy, but she managed to rally, breaking Arn immediately after the medical timeout and then again to take the match.
"I wasn't really at 100 percent," Goerges said. "I was sick the whole week but that's not an excuse.
"Greta played a very good match, which is what I expected because she's the champ here. It was a tough match and I was happy to somehow come through."
Sixth-seeded Roberta Vinci of Italy beat Rebecca Marino of Canada 7-5, 6-4, seventh-seeded Yanina Wickmayer of Belgium beat Karolina Pliskova of the Czech Republic 6-3, 6-4, and eighth-seeded Monica Niculescu of Romania beat American Jamie Hampton 7-6 (1), 6-1.