The US Open winner, 21, missed three championship points in the second set but regrouped to win 7-6 (7-2) 5-7 6-4.
The fourth seed broke for 2-1 in the decider, then served out to clinch victory in Melbourne.
Eighth seed Kvitova, 28, was bidding for her first major title since being stabbed in a knife attack.
The two-time Wimbledon champion, who said she was fortunate to be alive after the incident in December 2016, showed resilience to take the match into a third set as momentum swung from side to side.
Victory seemed to be inevitable for Osaka before Kvitova broke back for 5-5 on her way to winning 12 points in a row to lead for the first time since the start of the second set.
However, Osaka regained focus to take a decisive advantage in the decider, going on to replicate American Jennifer Capriati’s achievement of winning her first two Grand Slams back to back.
She missed a fourth championship point with a long return, but took the fifth when Kvitova hit a forehand wide.
A smiling Osaka dropped to her haunches on the baseline before returning to her chair and covering her face in shock as she savoured the moment.
Osaka, who replaces Simona Halep at the top of the rankings after the Romanian’s 48-week stint, becomes the first Asian player to be world number one.
She is also the youngest to hold top spot since Denmark’s Caroline Wozniacki, then aged 20, took the ranking in 2010.
(BBC)
