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.
Andreescu and Pliskova exchanged games again to make it 3-2 for the Czech player, but the Canadian seemed to have shaken off whatever had been bothering her legs earlier in the match.
Australia's top-ranked Ashleigh Barty lost Tuesday to ensure she would be dethroned in next week's rankings.
There was no such drama in Toronto, where Williams broke Osaka for a 5-3 lead in the first and closed out the opening set with a service victor.
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 sixth seed and former champion Elina Svitolina for her second top-10 victory if the week.
These two have split the previous two matches, as Andreescu won Miami this year in straight sets and Kenin won Acapulco of this year in three sets. On Thursday, she defeated world No. 5 Kiki Bertens.
Kenin, who ousted Barty this week, rallied back from 0-4 down in the first set and is two wins away from her third title of the year after triumphs in Hobart and Mallorca.
"I know what to expect from her", said Andreescu.
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"I've been practicing a lot on trying to figure out what to do in these kind of circumstances", Andreescu said. "It was a bit sore, but I think it got a little bit worse during the match", Andreescu said. "I didn't feel 100 per cent ready for the tournament because I had a long break (after Wimbledon)".
In the final four, Kenin will meet Canadian hope Bianca Andreescu, who won a quarterfinal clash with No. 3 seed Karolina Pliskova of the Czech Republic in three sets. But here I think I did a pretty good job adjusting to the conditions which weren't easy.
"It's hard not to focus on that when it's hurting at every point", said Andreescu. She battled to a 1-1 tie, but an overhand smash gave Pliskova a 2-1 lead.
Despite the circumstances heading into yet another decider, Andreescu held on, able to fight through and capitalize on Pliskova's mistakes, the most significant coming when she returned serve for match point directly into the net.
In the semi-finals Williams will face Czech qualifier Marie Bouzkova, who advanced when Wimbledon champion Simona Halep retired with Achilles tendon trouble after dropping their first set 6-4.
Later Friday, American Serena Williams beat Naomi Osaka of Japan 6-3, 6-4 in a rematch of last year's controversial U.S. Open final.
Ottawa's Gabriela Dabrowski and partner Xu Yifan of China beat Estonia's Anett Kontaveit and Hungary's Timea Babos 6-7 (0), 7-6 (5), 10-3 in the doubles quarterfinals.