Up next for Andreescu will be unseeded American Sofia Kenin, who extended her impressive Toronto run with a 7-6 (2) 6-4 win over Ukrainian former champion Elina Svitolina.
The 19-year-old Andreescu, from nearby Mississauga, advanced to 5-0 against top-10 opponents this year.
The 20-year-old Kenin upset top-ranked Barty in the first round. I've been off for seven weeks and being able to win these tough matches after that period off means so much.
Andreescu, who was playing in just her second match since returning from a shoulder injury that had kept her on the shelf since the French Open - 68 days between tour contests, in fact - displayed plenty of power en route to yet another heart-stopping victory. "I'm just going to go out there, try to enjoy myself, and give it all". "It was a bit sore, but I think it got a little bit worse during the match", Andreescu said. The Canadian scored her first break in the opening game, converted on another after holding and broke her opponent's service yet again before serving out the set and screaming "come on!" as she pumped her fist having completed the bagel.
Pliskova was absolutely annihilated in the opening set, a deer-caught-in-the-headlights with Andreescu's crafty point construction working wonders.
Windy conditions at Aviva Centre seemed to benefit Andreescu as Pliskova had to reset her toss on several serves in the first half. I felt it this morning, too.
Their quarter-final will be their first meeting since last year's US Open final when Williams argued with the umpire late in the match and Osaka was awarded a game as a penalty on her way to winning a first Grand Slam title.
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He said: "I have a friend at Juventus in Cristiano Ronaldo, he helped me a lot while I was there, both personally and on the pitch".
Pliskova beat Kontaveit in two sets after taking three against American Alison Riske on Wednesday.
Pliskova, who can reclaim the top spot on the WTA rankings with a solid run at the Premier 5 event this week, will face the victor between Canadian Bianca Andreescu and No. 5-seed Kiki Bertens of the Netherlands in the quarterfinals. It's going to be interesting to see how Andreescu responds physically given the wear and tear to get to this point.
Andreescu winced in pain on the court and hobbling between points, but her attempt to become the first Canadian women to reach the semifinals on home soil since Windsor, Ont.'s Faye Urban would not be denied.
"Achilles problems. I felt since the first match here".
Andreescu answered with an ace of her own to tie it up 4-4, then won another game when Pliskova's return on a break point was well past the baseline.
In the evening matches, American Serena Williams faced Naomi Osaka of Japan and qualifier Marie Bouzkova, also from the Czech Republic, played Simona Halep of Romania.
Unlike at Flushing Meadows previous year, where Osaka won her first Grand Slam title, there were no fiery exchanges with the umpire, no smashed rackets, no point or game penalties - just a rock-solid performance from Williams.