Things looked a little dicey at the beginning as Azarenka kicked off the match with a break, but Radwanska got right back on the horse, winning eight of the next nine games to build a 6-2, 2-0 lead.
Azarenka started to sink her teeth into the match a little bit at that moment, breaking back and staying even with Radwanska over the next four games to catch up to 4-2, but a love hold and one last break sealed the deal as the No.3-seeded Pole closed out the No.8-seeded Belarusian, 6-2, 6-2.
"I think it was a good match," Radwanska said. "I think everything was working for me today from the beginning. Playing an opponent like Vika, you really have to be focused from the beginning. There are no free points. I think I was really focused on my serve and trying to return well, as well.
"When I broke her, I would be really focused on my serve until the end."
Radwanska's game was as rock solid as ever - she put together a +10 differential in the match with 14 winners to just four unforced errors. Four unforced errors in 65 minutes - one every 16 minutes.
Azarenka, who was clearly hampered by a right knee injury, was -11 for the night (18 to 29).
"Every player's different," Radwanska said afterwards. "Everybody is playing different tennis. Of course, it depends also who is on the other side of the net. But I'm not really that powerful like the others, so I always have to find a way to win the game without serving at 200 kilometers per hour."
Despite her good feeling about this match, there are things she wants to improve going forward.
"No one's perfect," Radwanska said. "I guess there's always something to improve. When I'm going on court and practicing it's always everything. Not just one shot, one thing - it's always everything.
"I've had a few really good matches here. I don't feel like anything was really bad - there's nothing I've been thinking about the whole night, thinking about what I have to do to make it better.
"I just hope I'm going to play on a really high level again tomorrow."
And she'll need to - awaiting her in the semifinals is Ekaterina Makarova, who was two spots out of the seeds this week, but who has given her trouble in the past. Radwanska leads Makarova in their head-to-head, 3-2, but Makarova has won their last two meetings in straight sets, and on some very big stages too - the fourth round at last year's US Open and the same round at Wimbledon this year.
"We've played a couple of times, and the last time I lost, but here it's a different story," Radwanska said. "She's a very tricky player. Left-handed, so that makes it even more difficult. I just hope I play the same tennis I played today, and we'll see. I'll have to play aggressively against her, because she'll play aggressively against me. But she's also consistent and moves very well out there. We'll see."
? Aga Radwanska (@ARadwanska) August 9, 2014