Hingis sliced, lobbed and chipped her way to a 6-2, 7-5 win over Pauline Parmentier while Kuznetsova employed power tennis in a 6-3, 4-6, 6-0 victory over Camille Pin.
"You try to mix it up, to give the opponent a different look every time," said Hingis, who won the tournament a decade ago. "I think the crowd enjoyed it, too."
Kuznetsova had 46-6 edge in winners over her French opponent and a 34-9 advantage in unforced errors.
"I missed so many of my chances," she told reporters. "I've been missing so much. I was not moving my feet. But still I knew I was comfortable. I'll get it all together."
Former champion Andy Roddick, the fifth seed, celebrated his 25th birthday with victory over Argentine Jose Acasuso. The American was leading 4-6, 6-1, 6-2 when Acasuso retired with a knee injury.
Richard Gasquet was the first casualty of the day when the French 13th seed pulled out with a fever and sore throat. The withdrawal handed American wildcard Donald Young a walkover into the third round.
"I tried to practise today, but I couldn't play," Gasquet said. "I got a fever yesterday night. I can't play three sets in my match today. It's impossible for me."
Winners on a sunny day at the National Tennis Centre included seventh seed Nadia Petrova and number 11 Patty Schnyder on the women's side and number 19 Andy Murray on the men's.
Hingis was broken three times in the second set but returned the favor to her French opponent four times. In the third round, the Swiss will play 18-year-old Belarusian Victoria Azarenka, ranked 41st in the world.
"I don't feel like I can underestimate anybody out there," Hingis said. "Any opponent on a given day can come out and beat you."
After losing the second set to Pin, Kuznetsova needed only 23 minutes to win the final set and close out the match.
"It's not good second set, for sure," said Kuznetsova, the 2004 Open champion. "Well, when it happened, it happened. It was too late to change something.
"So I said, 'Nothing you can change.' So from that moment I just started to turn it on and just play the right shots."
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