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 six-time US Open champion Serena Williams or China's Wang Qiang for a place in Saturday's final at Flushing Meadows.
"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."
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 later quarter-final between Williams and 18th seed Wang.
"It would be exciting to play Serena one more time."