Third-seeded Azarenka, 22, saw off a powerful second-set fight-back by the Belgian mother-of-one to win 6-4, 1-6, 6-3. In Saturday's final, she will play either Maria Sharapova or Petra Kvitova.
"I felt like my hand is about 200 kilograms and my body is about 1,000 kilograms," Azarenka said, wiping away tears.
"Everything is shaking but that feeling when you finally win is such a relief. I can't believe it's over -- I just want to cry."
Azarenka has now gone one step better than her previous Grand Slam best of reaching the semifinals at last year's Wimbledon, and is one win away from becoming her country's first ever major-winner.
She has often faltered on the big stage, most noticeably at the 2010 Australian Open when she led eventual champion Serena Williams in the quarterfinals by a set and 4-0 before imploding.
But she stood firm Thursday to hold off Clijsters' revival and record the biggest win of her career.
"Before, I think you all thought I was a mental case but I was just young and emotional," she said. "But I'm really glad the way I fought. That's the thing I'm most proud of, I fought for every ball."
Azarenka came out with an obvious game plan to attack Clijsters' second serve and it paid dividends as early as the third game, when she broke with a clean forehand winner wide to the Belgian's backhand.
She kept on attacking Clijsters throughout the first set and was able to dictate the pace with her aggressive shot-making.
Azarenka won her service games easily while Clijsters struggled with hers, only winning 33 percent of her second serves in the first set.
The Belarusian won the opener in 49 minutes but Clijsters rallied in the second set as she cut down her error-rate and forced Azarenka into a series of long rallies.
She held her own serve and then broke Azarenka to love thanks to a string of unforced errors from the third seed, running away with the set and seeming to be on track to defend her title.
But the momentum swung again at the start of the third as Azarenka won her serve, then broke Clijsters to love, only to serve two double-faults on her way to giving the break straight back.
It was now Clijsters' turn to look nervous and although she was able to save three break points, a double fault on the fourth gave Azarenka a 3-1 lead.
She moved to 4-2 and had seven game points to open a 5-2 lead, but Clijsters refused to lie down and she got the set back on serve thanks to yet another unforced error from Azarenka.
But in a thrilling match Azarenka came again, breaking Clijsters to go to 5-3 and holding her nerve for a memorable victory, collapsing to the deck in tears as the Belgian put a backhand wide on match point.
Azarenka said earlier this week that she was in the best shape of her life after concentrating on her physical conditioning in the off-season.
She has also been able to shut out strong criticism of the screaming she makes when she hits the ball, which included large sections of the crowd mimicking her during her win over Australia's Casey Dellacqua.
Azarenka is the first Belarusian woman to reach a Grand Slam final since Natasha Zvereva finished runner-up at the French Open in 1988, representing the USSR.
She also has the chance to become only the ninth woman to win both the junior girls and women's singles titles in Melbourne, and the first since Australia's Chris O'Neil achieved the feat in 1978.