It is Radwanska's fourth consecutive venture to the last eight in Melbourne and she will need to be at her very best to make it any further; next up is her nemesis, Victoria Azarenka, who looked in superlative form whilst swatting aside Sloane Stephens earlier in the day.
However, Radwanska will draw plenty of comfort from the manner in which she dismantled her much-talked-about young opponent during Monday's closing act on Rod Laver.
In the previous round Muguruza had blown away former World No.1 Caroline Wozniacki admist a barrage of winners, and it was clear from the opening game that there would be no tempering of her aggressive instincts against Radwanska.
At first her gung-ho attitude looked like it would pay dividends. After pushing the Pole to deuce in her opening service game, Muguruza earned four break points in the next thanks to a series of unstoppable backhands.
Radwanska escaped that game and responded as only she can, defusing her opponent's dominant weapons with cunning and guile. An epic fourth game proved to be the turning point, Radwanska withstanding everything the Spaniard could throw at her before claiming the break.
From there, the No.5 seed went on a roll, holding for 4-1 before reeling off eight unanswered points to take the set. Muguruza briefly stemmed the tide at the start of the second, but the respite was only temporary.
Radwanska broke for a 4-2 lead before repeating the trick a few games later to wrap up a 61 63 victory.
"After those first four games, I was thinking that I'm going to spend three hours on court today," Radwanska said. "But I think that first break in the first set was the key.
"Really, she was playing such good tennis from the first point to the last one - really aggressive. I think as the match went on she started making some more mistakes but I still needed to concentrate 100%. Overall, I'm happy to close a match like that in two sets."
As well as she played, Radwasnka knows she will need to raise her game to yet another level if she is to overcome Azarenka, who has won the pair's last seven encounters.
"I think I have to play even better than today to beat her," Radwanska said of her quarterfinal opponent. "Obviously, she's playing great tennis, especially here, and is defending champion.
"I think I have nothing to lose. Hopefully I can really play my best tennis and I will fight."