Barty has a chance to return to the world number one position she held last week if she reaches Sunday's final after booking a semi-final spot on Saturday against either Czech third seed Karolina Pliskova or Russian Svetlana Kuznetsova.
Barty rallied from a set down in the previous round to defeat Anettt Kontaveit, but the reigning French Open champion is not stressing about the numbers, just concentrating on her steady tennis.
"I'm in the semis for the first time here," she said. "I'm not thinking of the ranking at all.
"I'm playing one match at a time. If I can win matches, the ranking will take care of itself.
"I've had an amazing three years with my team and an amazing season. I'm excited to be in new territory here in Cincinnati."
Top Greek player Sakkari came alive in the first set, battling from 5-2 down and winning 14 of the last 16 points to sweep the opener.
But Barty merely dug in to begin her fightback.
"I was more patient in the second and third sets. I served better, hit my spots," Barty said. "She was playing super-aggressive in the first set.
"I made a few simple adjustments, making her play a few more balls.
"I play my best tennis when my head is clear and I trust in my instincts. I can bring variety but get back to basics when I need to."
Barty defeated Sakkari with 29 winners and breaks on six of 14 chances over an hour and 45 minutes.