Gauff's serve proved decisive.
Osaka, now ranked 41, was unable to break the American's serve until late in the second set.
It meant 5-3 in the second set, in favor of Gauff.
Just like the first set, it was a 6-4 win for Gauff and the match victory after two straight sets.
At 5-1 in the second set, Coco Gauff also led 40-0 in the game.
But Naomi Osaka fought back against seven match points.
That impressed Gauff.
- It is very rare that someone comes back from 0-40 on two occasions.
But it's Naomi.
It just shows how much fighting spirit she has.
She could have thrown in the towel, but she didn't," Gauff told the WTA website, adding:
- I knew it would be tough against Naomi.
She is one of the best baseline players.
If she is going to win, it is on the long balls from the baseline that she wins.
I think I really stood my ground and won a lot more balls like that than she did today.
The win took Gauff to the quarterfinals of the WTA tournament.
For Osaka, it was an early exit, but she feels strengthened despite the loss.
- I realized during the match that I have let people call me mentally weak for so long that I had forgotten who I am.
But fighting like this is what I do.
I lost today but I feel very confident in who I am.
The press does not defeat me.
I am the press.
I'm very happy with that, Osaka said.