Safarova was the first of the two to advance, holding nine of her 10 service games and breaking three times to beat No.12 seed Sam Stosur, 64 64. Safarova has now won seven of nine career meetings with Stosur, including the last four in straight sets - Montréal last summer, then three times this year.
"I tried to believe I could do it from the beginning," Safarova said. "I've won the past few matches against her so I just had to concentrate again this time - because I really wanted to get this one too."
Two weeks ago Safarova won the Québec City title - her fifth WTA title, but first in over five years.
"Of course it helps - it had been a while since I won a tournament, and it was an amazing feeling in Québec," Safarova said. "I really enjoyed it there, and now it's such a nice feeling to play here.
"It's just a pleasure to keep playing more matches. I'm really enjoying it."
But extending her win streak to eight matches hasn't been easy - Polona Hercog served for their first round match at 6-5 in the third set before Safarova managed to grind out a 64 67(6) 76(2) victory in two hours and 47 minutes, then in the second round she could have easily gone to three sets as well, after No.8 seed Roberta Vinci stormed out to a 5-2 lead with set point. Safarova came back to win, 75 64.
"The first match was hard for me, coming from indoors to outdoors and a little bit of jet lag as well, but I'm feeling much better now," Safarova said. "I'm really just looking forward to the next one now."
The No.2-seeded Radwanska went on court a little later on against No.16 seed Dominika Cibulkova, sneaking out a very timely break at 4-all in the second set and serving out a 63 64 win over the Slovak.
There was more good news for Radwanska - her win over Cibulkova was her 400th career match win.
"Really?" a surprised Radwanska replied. "It feels like it was yesterday when I got 300!"
Does the World No.4 remember her first win?
"I have no idea, against who or when!"
Radwanska captured her 13th WTA title in Seoul last week and has now won seven matches in a row.
The only other completed match saw No.5 seed Angelique Kerber beat No.11 seed Ana Ivanovic, 64 62, which was also a little bit of revenge - Ivanovic had won all three of their previous career meetings.