The 29-year-old American booked a last-four berth in the WTA and ATP hardcourt event against the winner of a later match between US seventh seed Madison Keys and Greek fourth seed Maria Sakkari, who beat Canadian Leylah Fernandez 7-5, 6-2 in a rain-postponed match.
"I knew it was going to be a really tough match and that's what it was," Pegula said.
Pegula broke to open the final set and denied Svitolina on five break points in the sixth game before holding for a 4-2 lead.
Svitolina saved two match points before holding in the ninth game but Pegula saved a break point in the 10th game and advanced with a service winner on her third match point, improving to 3-1 overall against Svitolina after two hours and eight minutes.
"I was like, 'If I don't serve this out, it might have been a quick 5-7.' I probably would have lost," Pegula said.
"I was so tired. I know that sounds terrible to say. That's not what you're supposed to be thinking but... I sweated through the entire thing."
World number three Pegula, the 2019 Washington champion, reached her fifth WTA semi-final of the year and first since April on Charleston clay. Past success in the US capital helped her pull through, she said.
"It helps me feel more comfortable," Pegula said. "I've played a lot of matches on this court. I always love coming back.
"That definitely helps me dig my heels in a little bit."
Svitolina, 28, captured the first set on a forehand winner without facing a break point.
Pegula's first break chance of the match came on Svitolina's first service game in the second set, when the Ukrainian netted a backhand to put the American up 2-0 and she held from there to force a third set.
Svitolina, making a comeback after becoming a mother last year, is coming off a trip to the French Open quarter-finals and a victory over top-ranked Iga Swiatek in a Wimbledon semi-final run.
She ousted former world number one Victoria Azarenka in her Washington opener but was foiled in her bid for an 18th career WTA crown.
"Tons of respect for her," Pegula said of Svitolina. "She just had a baby. Everything she's going through with her country. I told her I feel like she came back as a new person. You can see the competitiveness."
The rain-hit men's side was hoping to play five round-of-16 matches and all four quarter-finals on Friday.
US top seed Taylor Fritz and Britain's Andy Murray, a three-time Grand Slam champion, were set for a last-16 meeting, as were hometown hero and second seed Frances Tiafoe and Chinese teenager Shang Juncheng.
American J.J. Wolf awaits in the quarter-finals for either Dutchman Tallon Griekspoor or France's Gael Monfils, the 2016 Washington champion. They were stopped by rain in the third set.
