Barty - who started the year ranked 271 in the world and will move into the top 30 for the first time - will face world No.1 and Wimbledon champion Garbine Muguruza or French Open champion Jelena Ostapenko in the semi-finals.
Second for match wins across all surfaces this season (49), behind Wozniacki (53), Pliskova handed a pivotal minibreak to 4-3 in the second set tiebreak.
Ostapenko is in great form having won her first hardcourt title last week at the KEB Hana Bank-Incheon Airport Korea Open in Seoul and now only Ashleigh Barty can stop her reaching a second successive final.
"I'm just happy to come through at the end", said the Australian.
Pliskova, the world No 4, saved three match points when Barty served at 5-4 in the third set, but the Australian recovered her poise and went on to dominate the deciding tie-break, which she won 7-2.More news: Bali evacuees surge as volcano threat grows
More news: Yosemite Rockfall Kills One Person, Injures Another
More news: Facebook sends team to Puerto Rico to get island back online
A brief pause to dry the courts following a rain shower couldn't save Muguruza, and Linette served the set out to love in the next game.
The 20-year-old recorded 29 winners to dismiss the reigning Wimbledon champion in 1 hour, 57 minutes. "She had a very good moment in the second set but that didn't disturb me to just keep going".
Muguruza, who had been hunting for her first victory as the top-ranked player in the world, found herself grappling with a knee injury that has plagued her for the past two weeks.
"When it gets tight or when I see myself going in the wrong way, sometimes I can go a little bit insane and lose my focus" she said earlier this week as the WTA Insider Courtney Nguyen revealed.
"I felt like I was close", said Pliskova in her post-match press conference.