Tsonga finished the match with nine aces and improved to 3-0 against Dimitrov. He will face Chinese qualifier Zhang Ze, who beat Li Zhe 6-1, 6-3.
"I didn't move really well, didn't hit the ball really good, but I was on the court with my head," said the seventh-ranked Frenchman, who won his first career match in Beijing in 2004. "The China Open is the story of my life."
Wozniacki was never threatened against Gajdosova, who committed eight double-faults and had 19 unforced errors. The Dane will meet Kaia Kanepi, who defeated Wozniacki last week in the third round of the Pan Pacific Open in Tokyo.
"The next match is a new match and we both start at zero-zero," Wozniacki said. "I go out there and find out what I have and hopefully it will be enough."
"I got more aggressive in the third set," said Zvonareva, who will face unseeded Ana Ivanovic. "I wasn't waiting for her to make mistakes any more and started playing my game."