Playing in combination for the first time in their careers, Williams and Wozniacki beat top-seeded Johanna Larsson of Sweden and Caroline Dolehide of the United States 6-2, 6-1, after defeating Nao Hibino and Makoto Ninomiya of Japan in their opening match.
The pair will not play together at the Australian Open, which will be Wozniacki's final Grand Slam tournament before retirement, save for an exhibition against Williams in Copenhagen, Denmark, in May. For that reason, the Auckland tournament offers the only chance for fans to savor the sight of two former world singles No. 1s playing as a partnership.
The match against Larsson and Dolehide, each an accomplished doubles player, was the toughest test of the Williams-Wozniacki partnership. Larsson has 13 doubles titles, and Dolehide has been a U.S. Open doubles semifinalist.
Williams was a driving force in their win on Wednesday, dominating the court, though she paid tribute to Wozniacki, who "never missed," according to Williams.
"We're just having a great time," Wozniacki said. "Even if I miss a couple and I'm mad at myself, Serena is always so positive. She's like, 'You're doing great. You're doing amazing,' so it makes you feel good out there.
"We're just going to go out there every match, just play, have fun and see what happens and the good thing is with doubles is we've had two matches and we're in the semifinals.''
Bouchard, who has been as high as No. 5 in singles, dropped out of the top 200 last year, at one stage losing 12 straight first-round matches. The 25-year-old Canadian showed signs of a return to form, as she beat Garcia in 88 minutes.
Bouchard incurred a time violation at set point in the first set but held serve, then closed out the match at her first opportunity.
Cornet sealed the match after 2 hours, 16 minutes with three consecutive aces.
"It just happened to be the best time to do my first aces of the match and three in a row, come on! I don't even know how that happened," she said.