Wozniak defeated Russian Vera Dushevina 6-2, 7-5. The Blainville, Que., native will face No. 25 seed Zheng Jie of China in the next round.
Jie came back to defeat Dubois of Laval, Que., 4-6, 6-4, 6-3.
In men's play, No. 21 seed Milos Raonic of Thornhill, Ont., was a game from eliminating Santiago Giraldo of Colombia, leading by two sets and 5-4 in the third when play was suspended due to rain.
Vasek Pospisil of Vancouver dropped a 7-5, 6-7 (5), 6-3, 6-4 decision to American Sam Querrey.
In men's doubles, Toronto's Daniel Nestor and partner Max Mirnyi of Belarus survived a scare in the first set to eventually beat Americans Michael Russell and Donald Young 4-6, 6-0, 6-2, 6-1.
The 56th-ranked Wozniak defeated Jie in the second round at the French Open. She owns a 2-0 record over Jie after winning their first match at Eastbourne three years ago.
Wozniak needed just 78 minutes to oust Dushevina, taking a 4-1 lead in the opening set and claiming the set with a winner after less than half an hour.
"Everything was going smoothly but she picked up her game at 6-2, 4-1," said Wozniak. "I was taking the ball a bit too far behind. But I was glad to finish it in two sets."
"Jie plays flat so I cannot allow her to dictate and I have to move her around if I'm going to win again."
Wozniak advanced with 17 winners to reach the second round at Wimbledon for the third time in six career appearances.
Dubois let her chances slip against Jie.
The Canadian could not hold her 4-2 lead in the second set as the Chinese pulled even at a set each after 90 minutes. The fight went out of Dubois in the third as she ended on a double-fault.
"I'm disappointed, I was very close in the second set," said Dubois, who will now return to Canada to prepare for the switch to hardcourt. "I had the momentum but it's frustrating when she takes it back. I'm not happy about that but overall it was a good match for me."
Dubois was broken eight times in the frustrating match, committing 22 unforced errors. She has been eliminated in the Wimbledon first round in four of five appearances.