Fifth seed Svitolina, 24, advanced to the last four at a second consecutive Grand Slam after matching her run to the Wimbledon semi-finals in July.
She will either play 23-time Grand Slam champion Williams or 18th seed Wang for a place in Saturday's showpiece final in New York.
"It feels amazing. It was a very, very tough match. We were both striking the ball well. It was quite even. In the end I had to close it out on my serve," Svitolina said. "I'm very, very happy the way I handled the pressure."
Svitolina watched a pair of match points pass her by at 5-3 on her opponent's serve as Konta gamely fought to stay alive, but the Ukrainian closed out victory in the following game.
"There was disappointment of course when I was close but I was just taking one point at a time and tried to stay calm."
Svitolina had already knocked out two-time former champion Venus Williams and 2017 runner-up Madison Keys and is in a class of her own as the only Ukrainian woman to reach this stage at a major.
She will attempt to emulate Andrei Medvedev as just the second Ukrainian to play in a Grand Slam final. Medvedev lost the men's 1999 Roland Garros final in five sets to Andre Agassi.
"It's going to be a good match tonight and it's a semi-final for me so I must enjoy it whoever I play," Svitolina said of the evening quarter-final between Williams and Wang.
"It would be exciting to play Serena one more time."
- Serena versus the field -
Williams, the lone former Grand Slam champion remaining in the draw, has defeated Svitolina in four of five previous meetings, although the latter won their most recent encounter at the 2016 Rio Olympics.
Konta, who took out third seed and 2016 runner-up Karolina Pliskova in the last 16, was denied in her bid to be the first British woman to make the US Open semis since Jo Durie in 1983.
Eighth seed Williams captured her last Slam title at the 2017 Australian Open while pregnant and hasn't won the US Open since 2014.
The 37-year-old American rolled her right ankle in a last-16 win over Petra Martic but said she felt "fine" ahead of a first-time meeting with Wang.
Williams holds a 99-12 career record at the US Open and is two wins shy of matching the all-time mark that belongs to Chris Evert.
Wang, 27, is trying to join Li Na, the former French and Australian Open champion, and Zheng Jie and Peng Shuai as just the fourth Chinese player to reach the last four of a major.
The US Open is guaranteed a first-time major finalist and there will be four different Grand Slam winners in a season in the Open era for an unprecedented third year in a row.
Canadian teen Bianca Andreescu, who hasn't lost a completed match since March, takes on in-form Belgian 25th seed Elise Mertens in Wednesday's quarter-finals.
Swiss 13th seed Belinda Bencic faces good friend Donna Vekic, the 23rd seed from Croatia, in the other last-eight clash.