After Victoria Azarenka, Serena Williams, Maria Kirilenko, Elena Vesnina and Svetlana Kuznetsova advanced earlier in the day, Wozniacki beat Ukrainian Lesia Tsurenko 6-4, 6-3 and in the battle of the young guns, Stephens prevailed over Laura Robson 7-5, 6-3.
Wozniacki's 6-4, 6-3 scoreline might look comfortable over Tsurenko, but the world No. 85 put up quite the challenge for the 10th seed.
Tsurenko especially put pressure on the Dane with her impressive backhand, but in the end 48 unforced errors to 19 winners proved to be her downfall.
Wozniacki capitalised to advance to the fourth round and to book in a berth against two-time Grand Slam winner Svetlana Kuznetsova.
The pair have met eight times previously on the WTA Tour with Wozniacki leading five to three. She did win four straight matches over the Russian, including at the 2009 and 2011 US Opens, but Kuznetsova did get a win back earlier this year in the second round in Sydney in three sets.
Wozniacki is looking forward to that challenge, but before focusing on that reflecting back on the challenge given to her from Tsurenko.
"It was tough for me to do much from her backhand because it was very flat and deep, so I just tried to make her move around a bit. She was returning quite well also so I was getting frustrated at the start," Wozniacki said.
"I feel like I have played better and better from every match and I'm just so happy to now be through to the fourth round. To have at least another match is great.
"I have played so many matches against her (Kuznetsova) and they are always tough. It's not going to be easy, but it's the fourth round and no match is ever going to be easy."
Without doubt, Stephens and Robson are two of the most exciting young talents in women's tennis but on this occasion the American 19-year-old showed that she is slightly more advanced than the 18-year-old Brit, who was born in Melbourne and for some time lived in Perth.
Stephens finished 2012 as the youngest player ranked inside the top 50 and as the only teenager, and after already having reached the fourth round at Roland Garros last year, plus the third rounds at Wimbledon and the US Open, she is a player on the rise with a bullet.
So is Robson. The 18-year-old is now ranked 53 in the world and her third round appearance at the Australian Open backs up a fourth round exit of the US Open last year.
She has long been a player earmarked for stardom having won the Junior Wimbledon aged 14 and then partnering Andy Murray at two straight Hopman Cup tournaments in Perth, highlighted by a singles victory over Spain's Maria Jose Martinez Sanchez in the final.
The meeting between Stephens and Robson in the third round is certainly a sign of the future with Stephens next to take on the winner of the Kimiko Date-Krumm and Bojana Jovanovski battle.