The 22-year-old fourth-round winner overcame an early wobble to defeat the 18-year-old Jovic 6-1, 6-4 in an all-American encounter played on a warm Labour Day night in New York.
Gauff, the 2023 US Open champion, made a nervous start when a double fault handed Jovic an early break in the opening game.
The advantage, however, did little to settle the teenager, who struggled to maintain her momentum as Gauff immediately found her rhythm.
The defending champion won the next six games in succession, combining aggressive shot-making with relentless movement to close out the first set 6-1.
Jovic steadied herself at the beginning of the second set, finally holding serve to avoid another early collapse.
But Gauff soon turned up the pressure.
Three outstanding defensive plays — in which she transformed seemingly desperate retrievals into attacking opportunities — helped her break Jovic for a 3-2 lead.
Jovic responded immediately by breaking back, showing the fighting spirit that has marked her breakthrough run at the tournament.
Gauff, however, refused to surrender control. She broke again to love before calmly serving out the match, completing victory in one hour and 33 minutes.
The result means Gauff has reached the quarter-finals without dropping a set at this year’s tournament.
Gauff praises teenage opponent
Despite the comfortable scoreline, Gauff was quick to praise Jovic, who is competing at the highest level of the sport at just 18.
“Iva's an incredible player, an incredible talent, she plays beyond her years. I'm used to being the younger American!” Gauff said.
Reflecting on her own performance, the 22-year-old described the opening set as particularly strong while acknowledging the improvement from her opponent in the second.
“I thought today was a good match for me. The first set was really high-level and she raised her level in the second.
“I had some opportunities to maybe get up some early breaks. We're all just happy with how I was able to close the last game out.”
Gauff also offered words of encouragement to Jovic, drawing from her own experience of competing professionally at a young age.
“I think I just remember when I was that age, every loss was so low, and every win was so high. I think there's lessons to be learned in the losses,” she said.
“She seems a little bit more mature than maybe I was at 18, but I feel like sometimes the losses for me felt so low.”
The American urged Jovic to take confidence from her performance rather than dwell on the defeat.
“So I think it's just important getting her to know that she's playing good-level tennis, and I think today it just went my way.”
Gauff added that early success does not always guarantee future results, saying Jovic would have plenty more opportunities to make deep Grand Slam runs.
“I am someone who played well young too, so it doesn't always matter. Sometimes it does matter, and you just learn those lessons and I know that she will be in many more fourth rounds and quarters, and she'll capitalise on those moments the next time.”
Andreeva awaits in quarter-finals
Gauff will now face French Open champion Mirra Andreeva in the last eight.
The American has dominated their previous meetings, winning all five of their career encounters, but she expects their latest clash to present a considerably tougher challenge.
“It is another tough match,” Gauff said.
“Mirra is someone that I always have tough matches with and they have leaned my way but every match could have almost gone either way.”
Andreeva enters the contest with greater confidence after winning her maiden Grand Slam title, and Gauff expects the Russian teenager to approach their latest meeting differently.
“She is obviously in a different mindset now at the top of the game coming off of a Grand Slam win. I expect her to approach the match completely differently than she did in the past.”
Women’s quarter-final line-up
With Gauff’s victory completing the last-eight field, the US Open women’s singles quarter-finals are now set.
Aryna Sabalenka will face Linda Noskova, while Jessica Pegula takes on Emma Navarro.
Gauff will meet Andreeva, while Qinwen Zheng faces Elena Rybakina for a place in the semi-finals.
For Gauff, the challenge now becomes even greater as she continues her pursuit of another US Open title — but her flawless record in sets so far means she enters the quarter-finals in impressive form.