The U.S. Open champion dropped only five points in the second set and then cruised through the decider.
"Maybe six months ago I wouldn't have been able to do that (come back)," U.S. Open champion Osaka said.
"I'm not sure if I'd have had the same feeling -- but six months ago I hadn't won the U.S. Open. Now I sort of know what could potentially come next.
"I feel like right now I'm really confident in myself... so I'm not that scared or threatened... this was an important win. It's harder for me to play against girls like her."
Osaka said players like Sevastova, who mix up their game rather than relying purely on power, have caused her trouble in the past and that Bajin's advice had helped her regroup.
"He said not to be so worried. It was acknowledging that she was playing really good and there was nothing I could do about that," Osaka, who takes on Lesia Tsurenko or Anett Kontaveit in the semi-final, added.
"I had to wait for my chance, and I think that's what I did really well in the second set."
In the men's competition, Osaka's compatriot Kei Nishikori battled past Grigor Dimitrov 7-5 7-5 in a rematch of the 2017 title clash in Brisbane.
Nishikori, seeking to avenge his loss in that match, staved off a comeback attempt by Dimitrov in the second set to improve his career win-loss record against the Bulgarian to 5-1.
"I want to go into the top five. That's my next goal... I think I'm playing great tennis again," world number nine Nishikori said.
Up next for Nishikori is France's Jeremy Chardy who moved in to the last-four by getting past Japanese qualifier Yasutaka Uchiyama 6-4 3-6 7-6(4).
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by Martyn Herman)
