Withi first seed Angelique Kerber, third seed Agnieszka Radwanska and fourth seed Simona Halep all out in Melbourne, Serena Williams is the only player ranked higher than Pliskova left in the women's draw.
Pliskova now faces Croatia's Mirjana Lucic-Baroni in the last eight.
Highlights: Pliskova sees off Gavrilova
"It was not my best but it's a win, so it counts," she said. "But for sure we all know I can play better. But it was enough. It was strange match, I would say, even from Dasha. I think she didn't also play really well today.
"Even I didn't feel my game that well, I still think it was sort of solid somehow."
The 2010 Australian Open girls champion could face Serena Williams in the semi-finals but said she was aware people were talking about her as a potential Grand Slam winner.
"I'm feeling confident, much better than I did in the grand slams before the U.S. Open. Everything is going my way now," she said. "Also with my form coming into this year, with winning the Brisbane, I was really playing well there."
Pliskova said the extra expectation did put more pressure on her. "I just don't want to think about it that much," she said. "These things and this talking doesn't win me the matches. But I would like to prove that the people who are talking about me, they are not wrong."