All the favorites breezed to victory during the early session of Thursday's WTA Rogers Cup action in Toronto.
Karolina Pliskova is now 2-0 as the world's No. 1 player although she was aided by an injury to her opponent.
The Czech star advanced to the quarterfinals when Japanese qualifier Naomi Osaka retired with an abdominal injury in the third set with Pliskova leading 6-2, 6-7 (4) 1-0.
Osaka had to withdraw from events in Prague and Madrid with the same injury.
Pliskova had 12 aces and did not have her serve broken in the match, but she received a bigger challenge than expected from the 19-year-old Osaka.
She admitted that remaining No. 1 will be a challenge.
"It's going to be tough," Pliskova told wtatennis.com. "There are a few tournaments to go before the end of the year and I know Simona's (Simona Halep) behind me. I'll do my best to stay there as long as I can -- hopefully a few more weeks."
Wozniacki attended Radwanska's wedding a few weeks ago and they are close friends, but Wozniacki did not show any mercy against her Polish opponent.
After Radwanska took a 2-1 lead in the first set, Wozniacki reeled off four straight games to take control.
Halep, the defending champion and second seed from Romania, also had an easy match, taking out Barbora Strycova of the Czech Republic 6-1, 6-0 in just 58 minutes.
Halep's quarterfinal foe will be Caroline Garcia of France, who eliminated 18-year-old American CiCi Bellis 6-4, 6-2.
In one other daytime match, Lucie Safarova of the Czech Republic defeated Ekaterina Makarova of Russia 6-3, 6-7 (3), 6-2.
Third-seeded Angelique Kerber was among those scheduled to play Thursday's evening.