The third seed from Belarus struggled to make any inroads against the more consistent Radwanska early on but upped her game impressively to progress 6-7 (0/7) 6-0 6-2.
The first set saw numerous breaks of serve with neither player capable of stringing more than two games together.
Pole Radwanska looked the more comfortable with the occasionally volatile Azarenka becoming frustrated with her game and the actions of the crowd, who were again mocking her grunting.
Azarenka held it together to break for a 6-5 lead only to be broken herself as Radwanska took it to a tie-break she dominated as her opponent's powerful baseline game fell apart.
In previous years, that would often signal the beginning of the end for Azarenka but her new-found maturity again came to the fore as she bounced back in determined fashion, reeling off seven games on the spin to level it up and edge ahead in the decider.
Radwanska broke the slump to level it at 1-1 but Azarenka nudged 3-1 up and then broke again for 5-2.
She held her nerve impressively when serving it out to advance to the last four for the first time in Melbourne.
"We just cannot play two sets, we have to push each other to the limit," she said.
"We played some great tennis and I am really glad I could stay tough and see it out at the end.
"I am a year older and wiser, so I take it step by step, play every point and give the best I can and the result will be the result."
As for the crowd, Azarenka was in forgiving mood, adding: "The crowd don't distract me at all, thank you for being here, it means a lot."