The top-ranked Williams waltzed past Belgian Alison Van Uytvanck 6-0, 6-4 at Melbourne Park.
The 18-time Grand Slam champion and reigning U.S. Open titlist is seeking her first title in Melbourne since 2010. One more Grand Slam title and she would pass Chris Evert and Martina Navratilova on the all-time list of champions.
"If I could get to 19 in Australia that would be amazing," Williams said.
Up next for the American great will be former top-10 star Vera Zvonareva, who lost to Williams in the 2010 Wimbledon final.
The reigning Wimbledon champion Kvitova recorded her 65th career Grand Slam victory with a 6-1, 6-4 decision over Belgium's Richel Hogenkamp, while the eighth-seeded U.S. Open runner-up Wozniacki topped American Taylor Townsend 7-6 (7-1), 6-2 on Day 2.
Kvitova, fresh off her title in Sydney last week, will be opposed by German Mona Barthel in her next outing, while Wozniacki's second-round opponent will be fellow former No. 1 Victoria Azarenka.
The unseeded two-time Aussie champ Azarenka got off to a fine start this week by pasting American Sloane Stephens 6-3, 6-2. Azarenka titled back-to- back here in 2012 and 2013 before being slowed by a foot injury last year.
Meanwhile, sixth-seeded former Wimbledon runner-up Agnieszka Radwanska dispatched Japan's Kurumi Nara 6-3, 6-0 and 11th-seeded 2014 Aussie Open runner-up Dominika Cibulkova came from behind to best Belgian Kirsten Flipkens 3-6, 6-3, 6-1. Cibulkova lost to since-retired Li Na in last year's finale in Oz.
Venus Williams, the former No. 1 who is seeded 18th at this fortnight, took care of Spaniard Maria-Teresa Torro-Flor 6-2, 6-2. Venus, an Aussie runner-up to her younger sister Serena in 2003, opened her 2015 season with a title in Auckland two weeks ago, beating Wozniacki in the final.
Venus' second-round opponent will be fellow American Lauren Davis.
In other seeded action Tuesday, American Madison Brengle, last week's runner- up in Hobart, ousted No. 13 Andrea Petkovic 5-7, 7-6 (7-4), 6-3; No. 19 Alize Cornet defeated Zhang Shuai 6-3, 6-2; No. 20 Aussie Samantha Stosur beat Monica Niculescu 6-4, 6-1; No. 24 Garbine Muguruza topped Marina Erakovic 7-5, 6-0; No. 25 Barbora Zahlavova Strycova dismissed Timea Babos 6-4, 6-4; No. 26 Elina Svitolina erased Jana Cepelova 6-3, 7-5; No. 29 Aussie Casey Dellacqua cruised past Yvonne Meusburger 6-4, 6-0, and No. 30 American Varvara Lepchenko vaulted past Vitalia Diatchenko 6-3, 6-3.
Several other women advanced, including Americans Coco Vandeweghe, Irina Falconi and Madison Keys, who defeated Ukrainian Lesia Tsurenko 6-3, 7-5.
The second round will commence Wednesday, including matches for second-seeded former No. 1, former Aussie champ and two-time runner-up Maria Sharapova, third-seeded French Open finalist Simona Halep and seventh-seeded Canadian star Eugenie Bouchard. Sharapova will take on fellow Russian Alexandra Panova, while Halep will meet Aussie Jarmila Gajdosova and Bouchard will battle Dutchwoman Kiki Bertens.