Barty will on Tuesday play Petra Kvitova in a re-match of a quarter-final here a year ago won by the Czech.
Barty took revenge over the 18th-ranked Riske after losing to the American last summer at Wimbledon.
World No. 1 Barty said that wind blowing form one end of the court made play a challenge.
“It was playing very different from each end of the court. I just had to hang in there and give myself a chance.
“The wind made it exceptionally hard from one end, but you have to be smart and use it. I was struggling sometimes.”
Barty was untroubled in the opening set as she faced the gusts on the Australia Day holiday.
The momentum shifted in the second set as Riske flipped a switch with a double break to square the evening at a set apiece.
Barty took a 3-1 lead in the final set, backing it up with a love game for 4-1. But a hold from Riske and a break-back put the match back to level pegging in the tight closing stages.
Barty advanced to the thrill of the crowd with a concluding break of Riske in slightly more than 90 minutes and the American sent over a double-fault on a Barty match point.
The Queenslander will be working not to let her chances here go to waste in the next round.
“It was an incredible year for me in 2019. Another opportunity for a Grand Slam quarter-final doesn’t come along every week,” the reigning Roland Garros champion said.
2019 runner-up Petra Kvitova rallied from a set and a break down to survive a fast start from Greek Maria Sakkari, with the Czech seventh seed advancing to the quarter-finals 6-7(4), 6-3, 6-2.
The match was played in the raucous atmosphere created by Greek fans.
“When I was shaking the hand with the umpire, I told him it was like a soccer match today, Kvitova said.
“In one way, it’s nice, but this is tennis, and it’s not a Fed Cup. It was strange, but it didn’t bother me at all.”
The Czech still needed to recover after being pout on the back foot in the early stages.
Kvitova kicked off the Australia Day holiday with her victory in two and a quarter hours.
“There were a lot of nerves out there. I didn’t feel the best, the winner said. “I was just too tight, everything was flying somewhere.
“But with time I got used to it and started to play a little bit better, more freely.”
The fightback took shape as she won six consecutive games for a 3-0 lead in the third set to reverse the momentum against her 23rd-ranked opponent who was bidding to become the first Greek woman to make the quarters at a Grand Slam.
The seed advanced on a third match point after Sakkari lost serve after saving two match-winners from her opponent.
“At the end of the day it was about fighting spirit in a way,” Kvitova said. “Even if I didn’t play my best, Maria played really great tennis.
“I’m so happy that in the end I felt my game again.”
Sofia Kenin ended the run of Coco Gauff as she sent the 15-year-old out 6-7(5), 6-3, 6-0, fighting through a comeback to advance on a second match point
The Moscow-born American reached the quarters at a major for the first time in the face-off between two Florida-based players.
Gauff, youngest player to beat a defending champion at the Australian Open in the Open Era, showed little of the form which led to her third-round knockout of holder Noami Osaka.
The American ended with 48 unforced errors, well over twice as many as Kenin’s 22, with the winner getting slightly emotional at the end..
“It meant a lot to me. I was just so happy to have won. It was a tough match. I knew she’s playing well,” Kenin said.
“I was just really happy with the way that I was able to handle my emotions and just fight through every point.
“I’m just so happy that I won,” added the three-time 2019 titleholder.
Kenin, 21 and ranked 15th, worked to ignore the hype around Gauff, who knocked out defending champion Naomi Osaka in the previous round.
“She’s 15, there a bit of the age difference. She has a lot of hype, she has a big name. Obviously she’s playing well.
“I just tried not to let that get the better of me, just try to take it like any other match, focus on myself, focus on my game, grind it out basically.”
Gauff copped the loss as part of her tennis learning curve.
“I was disappointed, but I don’t really think anything of Naomi or my previous matches had anything to do with it.
“When I lose, I’m just a bit emotional. I know that I’m capable of coming back. In the second round I was down.
“I’ve improved since Auckland (this month) to now, even though it was a short amount of time, just a week. I honestly feel like I improved a lot in that week.
“With more training, I’m sure I’ll do better.”
Another spoiler fell in the fourth round, with China’s Wang Qiang going down to Tunisian outsider Ons Jabeur 7-6(4), 6-1, leaving the winner the first Arab woman to get this far at a major.
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