The Blainville, Que., native will face top-seeded Victoria Azarenka in the next round.
In men's doubles play, the top-seeded team of Daniel Nestor of Toronto and Max Mirnyi of Belarus defeated Dutchman Robin Haase and Finland's Jarkko Nieminen 6-3, 6-4.
Wozniak dominated in a near-flawless first set and overcame a lapse while leading by a break in the second. That miscue was partly caused by a long injury timeout taken by the No. 34-ranked Zheng with Wozniak leading 3-2.
The pause left Wozniak to practise her serve on the court while a doctor and trainer spent at least 10 minutes examining and patching a heel blister on Zheng's left foot.
Wozniak managed to get her concentration back when play resumed despite exchanging breaks with her opponent.
A concluding break in the final game put the Canadian ahead and Zheng sent a forehand long to end the match.
"I'm content with this win," said Wozniak. "But the injury time was very long. You cool off a bit when that happens. After she was treated she still moved well, so it was not an easy win.
"I came back and tried to keep the pressure on her. I played a good game at 4-4 to lead 5-4 and I finished it off well. It felt good to keep up the pressure."
Wozniak won with 21 unforced errors and 20 winners, but committed six double-faults. She broke four times.
Wozniak and Azarenka have never met at the WTA level, but played frequently in their junior days with the Canadian losing their first four meetings starting in 2004 in Wimbledon juniors.
The Canadian won their last match — six years ago in Pittsburgh at the Challenger level — advancing as Azarenka retired in the second set.
"It will be important to come out and only focus on my own game," said Wozniak. "I can't let her game or anything else bother me. I have to focus on each point and mix it up.
"She was always tough in juniors. You cannot let her dictate play, you have to move into the rallies early and try to end the point."
Azarenka said she is expecting a tough battle.
"She's a very difficult opponent who's been showing some real good tennis in the past," said the Belarusian. "I know she has had big wins in her career."
"I've played her many times before, she's a tricky opponent so I definitely have to come up with good tennis in my next round, and we'll see. But I'm excited to play against her again."
The win marked the fourth time Wozniak has advanced to the third round at Roland Garros, with her best performance a fourth-round showing in 2009 where she lost 6-1, 6-2 to Serena Williams.
Wozniak won her doubles match later in the day. She teamed with Romania's Simona Halep for a 6-2, 6-3 win over Britain's Anne Keothavong and Alexandra Cadantu of Romania.
Note to readers: This is a corrected story. A previous version had incorrect player names in the penultimate paragraph