Gauff won 6-0 6-2 in 67 minutes against Latvian 20th seed Ostapenko to record her best run at the tournament.
The 19-year-old will now face French Open runner-up Karolina Muchova for a place in the final.
“I think the problem in the past in Grand Slams is that I would emotionally be drained,” sixth seed Gauff said.
“Now I’m physically fresh and emotionally fresh, and I think that just came from experience.”
Another victory would put Gauff into the second major singles final of her career, matching her run at the 2022 French Open when she was beaten by Poland’s Iga Swiatek.
There has been a different aura about Gauff following a successful North American hard-court swing where she won two of the WTA Tour’s biggest titles in Washington and Cincinnati.
Since a chastening first-round exit at Wimbledon, Gauff has turned her form around with the help of new coach Pere Riba and consultant Brad Gilbert.
The teenager has won 16 of her 17 matches since losing at the All England Club in early July.
Gilbert, who has coached Andy Murray and Andre Agassi among others in a successful career, has been the focus of a lot of the attention and Gauff credited him for helping her enjoy her tennis more.
“I wish I embraced the fun parts a little bit sooner,” said Gauff, who was left in tears when Ostapenko beat her in the Australian Open fourth round earlier this year.
“I thought to play and win you have to be ultra serious and ultra focused, which that is true, but also you still have to enjoy it.
“I think that’s what’s been the change is that I’m having more fun.
“One of the first things Brad said is ‘you need to smile more’, it wasn’t really anything with my game.
“That’s something I’m trying to work on and continuing to do, and obviously I think it’s helping my results.”