Victory meant Vekic reached her maiden Grand Slam semi-final and became only the second woman from her nation to do so at the All England Club, as she matched Mirjana Lucic's 1999 feat, but it was not all smooth sailing for the unseeded 28-year-old.
Sun saved three breakpoints under the Court One roof and broke for a crucial 6-5 advantage before digging herself out of a hole again to seize the opening set on serve with the most delicate of drop shots.
The Te Anau-born left-hander surrendered her serve in the eighth game of the next set before Vekic made a flurry of double faults while serving for the set, only to regain her composure and draw level in the match with another break.
Lulu Sun's astonishing run from qualifying tournament to last-eight Wimbledon showpiece is over. (AP PHOTO)
The match turned on its head when Vekic broke in the third set following a double fault from Sun's racket, and the former Australian Open and US Open quarter-finalist quickly pulled away for a 5-0 lead.
She duly settled the contest on serve to dash Sun's hopes of becoming the first female qualifier to make the Wimbledon semi-finals since American Alexandra Stevenson 25 years ago.
Vekic, who has struggled to get back to her best after knee surgery in 2021, said: "Those couple of years were very tough. I didn't think I was ever going to come back to the level that I even had last year.
"So reaching my best result ever at a Slam, I'm really proud of myself, of the work that I've done, of the work that my team has done. I'm very thankful to them for believing in me when I didn't."
Vekic now plays seventh seed Jasmine Paolini, who blazed past American Emma Navarro 6-2 6-1 in only 58 minutes to become the first Italian woman to make the Wimbledon semi-finals.
The 28-year-old's victory ensured she eclipsed compatriots Camila Giorgi (2018), Francesca Schiavone (2009), Silvia Farina Elia (2003) and Laura Golarsa (1989), who had all reached the quarter-finals at the grasscourt Grand Slam in the Open era.
Jasmine Paolini celebrates becoming the first Italian woman to reach the last four at Wimbledon. (AP PHOTO)
"It's amazing to get the win on this special court and I'm so happy to be in the semi-final," Paolini said.
"It's so special, a dream to be here in this position. I was watching finals on this court when I was a kid, it's strange to be here."
Before this year Paolini had never won a match on grass, or gone beyond the second round of a major tournament.
