She is also the first Asian player to be world number one, and the youngest player to hold top spot since 2010.
But Osaka steadied herself after a trip to the locker room before the third set.
From the start of their player-coach relationship, Bajin "was very positive and I was really happy about that because I tend to (get) down on myself a lot", she told the tournament's official website after the match. Last year, at the same tournament, Osaka was No. 72 in the world.
More poignantly, it was her first such appearance since December 2016, when an intruder at her home in the Czech Republic cut her left hand - the one she uses to play tennis - so badly that hours of surgery were required to fix it. However, fast forward four months and the big-hitting fourth seed was back on the biggest stage with the chance to enjoy her finest moment at the Australian Open.
Kvitova, 28, knows what it's like to be the centre of attention. But for the first time, it would go her team's way as the Czech came up with a strong second serve to force the tiebreak.
For a while Saturday it looked as if her moment would again be taken away from her, this time through play on the court rather than drama off of it. I'm just a tennis player playing another tennis player. And her bulging trophy cabinet.
Osaka had nothing but nice things to say about Kvitova after the match.
Osaka, who went into the match with a record of winning 59 straight matches after taking the first set, broke again to take control as Kvitova´s error rate climbed.
The sulking that spoiled her exit in Brisbane earlier this month reared its head when she wasted three championship points and then got broken at 5-3 in the second set, slamming her racquet into her knees.
Osaka, who the Japanese public may perceive as being free-spirited, is at her core a perfectionist, and followed through with the tough training program that Sillah put her on.
How pivotal was that moment?
Kvitova was 21 when she made her Grand Slam breakthrough at Wimbledon in 2011 and was a star on the rise, much like Osaka is now. Osaka, meanwhile, entered the day having won 59 matches anywhere after going up by a set. Turned out, that wasn't the case. "It's just how it is", she said. "I didn't have a choice".