The teenager is making her Grand Slam debut in Melbourne and beat China’s Peng Shuai in straight sets in the first round.
Highlights: Teenager Kostyuk gets past Rogowska
She is the youngest player to reach a Grand Slam third round since Mirjana Lucic-Baroni in the 1997 US Open.
Martina Hingis reached the quarter-finals in Australia as a 15-year-old in 1996.
Kostyuk is ranked 521 in the world but will race up the WTA standings after the Australian Open. She plays fellow Ukrainian and fourth seed Elina Svitolina in the next round.
Appearing completely at ease during her post-match media duties, Kostyuk said she still had to process her achievement before worrying about her next round.
"I still didn't think about that match," she said. "I'm still, with emotions, I'm still with this match, and it's my sixth match here. I feel like with every match, I'm doing better and better."
The daughter of tennis parents, home-schooled Kostyuk is managed by Ukrainian former top-10 player Ivan Ljubicic, a member of Roger Federer's entourage.
"I didn't feel like she was 15 at all," Rogowska told reporters. "Yeah, honestly, the power of her shots were - I didn't feel like she was 15, but obviously, yeah, she's swinging freely ... I feel she's going to be a dangerous player when she grows up."
Marta Kostyuk - Australian Open 2018
Image credit: Getty Images
Despite her comprehensive win over the Australian, Kostyuk said she had struggled to control her emotions and was fuming when given a code violation for coaching after her mum gestured at her from the players' box.
"I was so mad, because I didn't see what mom was showing me. Then when the referee said code violation, I was, like, 'What? I didn't even see her, like - like, I swear I didn't see what she was showing me'."
After the match, her mum made another intervention, swiping her phone away from her before she could check congratulatory messages.
"Well, I take the phone, and I had to eat at the same time," said Kostyuk. "My mom told me leave the phone and eat properly. Because I didn't have normal breakfast, that's why I felt quite bad today on court."
Elsewhere, seed slayers Belinda Bencic and Zhang Shuai were brought back down to earth at the Australian Open on Wednesday.
Swiss Bencic, who knocked out last year's runner-up Venus Williams on a day of shocks on Monday, slumped to a 6-1 6-3 defeat by Thai qualifier Luksika Kumkhum.
Zhang, conquerer of U.S. Open champion Sloane Stephens in round one, was also toppled by a qualifier in the shape of Czech Republic's Denisa Allertova. Allertova won 6-4 7-6(5).