A few hours on from World No.1 Angelique Kerber's shock loss to Daria Kasatkina, Radwanska overcame a slow start - and a brief rain delay - to wrap up a 7-6(1), 6-1 victory in Tuesday's evening session.
"I was struggling with a couple of things tonight, but a very good tie-break from my side, very pleased with that," Radwanska said. "Obviously it was much better in the second set, more comfortable and confidence. It was also a couple of tight games but in the end I was the one who was make the right shot. Very happy to make that match in two sets."
Last week in Shenzhen, Radwanska surrendered her title to Alison Riske, and early on against McHale it appeared the after-effect was still lingering. However, the Pole produced a magnificent response to dropping the opening three games, delving into her box of tricks to pinch the first set and rattle through the second.
? WTA (@WTA) January 10, 2017
The Pole's progress was temporarily halted by a shower at 4-1. This delay failed to break her concentration, and on the resumption she broke once more before wrapping up victory with a pin-point forehand.
Her reward is a quarterfinal meeting with the tournament's surprise package, qualifier Duan Ying-Ying, and earlier 6-3, 6-2 winner over CoCo Vandeweghe. In Shenzhen, Radwanska came within a point of losing to Duan and will be taking nothing for granted in the rematch."
"[Against Duan] now I know what to expect. We played for the first time last week and that was a three-hour battle. I was one point from home. Now I know what to do and how it's gonna be. I'm just going to enjoy the game."