The hard-hitting Belarusian collapsed to the court in tears after winning 4-6, 6-3, 6-4 against the Wimbledon champion in a high-quality 2hr 28min arm-wrestle on Rod Laver Arena.
The 24-year-old Sabalenka wiped a tear from her right eye before getting a warm hug from Moscow-born Rybakina, who played a full part in an amazing match between to hard-hitters.
"Thank you, my team, the craziest team on the tour. We've been through a lot of, I would say, downs last year," Sabalenka said, addressing her team after receiving the trophy.
"Thank you so much for what you are doing for me. I love you guys."
Turning to beaten 22nd seed Rybakina, she added: "You're such a great player and of course we are going to have many more battles, hopefully in finals of the Grand Slams."
Sabalenka will now rise to second in the world rankings behind Poland's Iga Swiatek, equalling her career high, having triumphed in her first Grand Slam final.
"I need a few more days to realise what just happened," Sabalenka told Australia's Channel Nine.
"Oh my god, I'm speechless, to be honest. I was super emotional at the end."
Sabalenka, the fifth seed, then ran to her player's box to celebrate joyously with her team.
It was a fitting finale to two weeks of drama at Melbourne Park, highlighted by brutal groundstrokes, precision serving and wonderful rallies from two players at the top of their game.
'Take a deep breath'
Rybakina cruised through the first set in just 34 minutes but Sabalenka scrapped her way back in a 57-minute second set to take it to a nervy decider.
It was then a case of which of the big servers would blink first in a tremendous toe-to-toe battle.
At 3-3 Rybakina -- who represents Kazakhstan-- could not find enough first serves and though she saved two break points, a third was too much and Sabalenka had the finish line in sight.
An ace took her to 5-3 and Rybakina held to force Sabalenka to test her nerves and serve for the championship.
She was up to the challenge, but needed four nerve-shredding match points after a display where she hit an astonishing 51 winners and 17 aces to edge past the big-serving Rybakina.
"I just kept telling myself that nobody said this is going to be easy. She's going to fight, this is the final, just work for it," Sabalenka said afterwards, describing how she got through those four match points.
"Take a deep breath and just work.
"I was just super happy that I was able to handle all the emotions in the last game, it was super tough for me," added Sabalenka, who had reached three Grand Slam semi-finals before this year but never gone farther.
She suffered nerves in the past and struggled badly with her serve last year.
"They were really tough matches and I just couldn't understand until right now that I really needed that to understand what I have to change," Sabalenka added.
"I now know what else I have to work on and I'm just super happy right now to break through this wall."
Sabalenka will now rise to second in the world, equalling her career high.
Rybakina will have the consolation of breaking into the top 10 for the first time, after reaching her second Grand Slam final in seven months.
She was awarded no ranking points for her Wimbledon win because of the ban of Russian and Belarusian players there.
