World No. 2 Wozniacki produced a great escape against little-known Croat Jana Fett, saving two match points and rallying from 5-1 down in an epic third set to keep her dream of a first Grand Slam title alive.
She looked out for the count, and was struggling afterwards to work out how she survived 3-6, 6-2, 7-5 against a player ranked 119.
Fourth seed Svitolina also came from a set down to overcome spirited Czech Katerina Siniakova 4-6, 6-2, 6-1.
The Ukrainian is now on a seven-match win streak after winning the lead-up Brisbane International.
She picked up five WTA Tour titles last year, more than any other woman, making her a serious Grand Slam contender.
Her next task is tackling 15-year-old sensation Marta Kostyuk, who became the youngest woman to reach the third round since Martina Hingis got to the quarter-finals in 1996.
Also Ukrainian, she beat local wildcard Olivia Rogowska 6-3, 7-5.
Former winner Jo-Wilfried Tsonga fought back to vanquish rising Canadian star Denis Shapovalov in a five-set thriller, 3-6, 6-3, 1-6, 7-6 (7/4), 7-5.
He will face either Australian 17th seed Nick Kyrgios or Serbia’s Viktor Troicki in the third round.
MORE SEEDS FALL
On a hot Melbourne day, Croatia’s sixth seed Marin Cilic also advanced to the third round, with last year’s Wimbledon finalist easily beating Joao Sousa.
US Open semifinalist and 10th seed Pablo Carreno-Busta also went through after French veteran Gilles Simon retired injured when trailing 6-2, 3-0. But Russia’s Anastasia Pavlyuchenkova, a quarter-finalist last year, became the latest seed to slump out in the women’s draw, which has been shorn of leading names over the first two rounds.
Seeded 15, she lost to Ukraine’s Kateryna Bondarenko.
Venus Williams’ conqueror Belinda Bencic also ran out of steam, having no answers against Thai qualifier Luksika Kumkhum, slumping out 6-1, 6-3.
Rafael Nadal resumes his march towards a 17th Grand Slam later on Rod Laver Arena, after dispelling any lingering injury concerns in his opening match.
The world number one faces Argentina’s Leonardo Mayer, who has never gone beyond the second round at seven previous attempts at Melbourne Park.
Last year’s finalist Nadal has said his body was feeling ”good” and he had ”no problems” with his troublesome knee.
Surprisingly, he is not the prime time men’s night match on centre court, with that honour going to third seed Grigor Dimitrov, who takes on American Mackenzie McDonald.
The stylish Bulgarian admits he dreams about winning a Grand Slam, but so far has never got beyond a semi-final.
”I’m going to deal with it. That’s all I’m really focusing on,” he said about his drive to break his Grand Slam duck.
French Open champion Jelena Ostapenko is also in action later, along with Australian Nick Kyrgios who was slapped with a $3,000 fine Wednesday for swearing in his first round match.