A marathon first set took 1hr 17min before the world number one completed her 7-5, 6-1 triumph in 1hr 47min. She will face either Serena Williams and Sloane Stephens for a place in Saturday's final.
The very first game was a drawn-out scrap, lasting eight minutes and going to Russian comeback queen Kuznetsova, a two-time major-winner who is making a successful return from injury.
She survived pressure in her opening two service games and broke Azarenka in a fourth game that stretched to 15 minutes and included 10 deuces. After 34 minutes, only four games had been completed, with Kuznetsova leading 3-1.
Azarenka then trailed 1-4 but she broke back to peg the deficit to 3-4 as errors crept into Kuznetsova's previously steady onslaught. Another break gave Azarenka a 6-5 lead and she held her nerve to close the set.
The Belarusian began motoring to victory when she broke Kuznetsova's opening serve of the second set. She immediately conceded her own serve, but another break was exchanged and that was the end of Kuznetsova's resistance, as Azarenka finished the match with a barrage of groundstroke winners.
"She played really well throughout the whole match," Azarenka said. "At the beginning, it took adjustment because she plays such a different game.
"I'm glad I fought through and produced my best tennis when it was needed."
The unseeded Kuznetsova took a 4-3 win-loss record into the match. The former French Open and US Open is undergoing a career resurgence at the age of 27, making a mockery of her world ranking of 75 by beating number 10 Caroline Wozniacki in the fourth round.
Her lowly standing at the end of an injury-marred 2012 was the first time in 11 years she was outside the top 50. But although she pushed Azarenka to the limit, the defending champion hung tough.
"It is the fire I have," the world number one said. "I have so much passion for the game since I was a kid. I wouldn't leave the court until 10 o'clock at night.
"But it is important to keep calm and keep humble in this sport."
The top ranking is up for grabs at Melbourne Park between Azarenka, number two Maria Sharapova and number three Serena Williams.
Azarenka is defending her points from winning the Australian Open last year, and must retain the title to extend her 48-week stay at world number one. Williams is assured of the top spot if she reaches the final.