De Minaur, the world number six from Australia, fell to American Nakashima 7-6 (7/5), 6-4 in a rematch of last year's Washington quarter-final.
"He came out with some great serving, a lot of first serves," the top-seeded Aussie said. "I played at a high level. I just threw in two pretty awful games on my serve.
"It's a little bit frustrating, but you live and you learn."
World number 33 Nakashima booked a Saturday semi-final against the winner of a later all-American match between 10th-ranked Taylor Fritz and world number 40 Alex Michelsen.
Nakashima, whose only ATP title came at San Diego in 2022, never trailed de Minaur in the tie-break and fired his eighth of 10 aces to take the first set.
Nakashima broke in the ninth game of the second set, then held on a service winner to end matters after one hour and 54 minutes.
"He's a very quick and explosive player," Nakashima said. "I knew I had to serve well at the crucial moments and try to be aggressive."
The American fired 31 winners to 22 from De Minaur and saved six of seven break points he faced in improving to 3-1 in their personal rivalry, including a Queen's quarter-final triumph in June.
"I was probably playing better, having better stats on top in the first set, and it just slipped away," de Minaur said. "In the second set I've got my chances. Break points, just can't convert. All of a sudden I throw in a bad game, and that's the match."
WTA
World number three Pegula, an American who won her first career WTA title at Washington in 2019. eliminated 20th-ranked Anna Kalinskaya 6-3, 7-5, to reach her sixth WTA semi-final of the year.
"Since the beginning of the year I'm finding more confidence in matches hitting different spots," Pegula said. "I was focusing on that a lot today."
Pegula, who fired 24 winners against 17 unforced errors with six aces, will face the winner of a later match between Russians Diana Shnaider and Liudmila Samsonova on Saturday for a berth in Sunday's final.
Pegula seeks her 12th career WTA crown and third of the year after triumphs in Dubai and Charleston.
The American led 2-1 when Kalinskaya took a medical timeout for treatment on her right foot. Pegula broke in the fourth game and held from there to take the first set in 37 minutes.
Pegula was serving for the match in the 10th game of the second set but fell behind 0-40 to face her first break points of the day. She saved three but then, on a fourth, sent a backhand long to deadlock the match at 5-5.
Kalinskaya gave back the break on her third double fault of the 11th game, and Pegula held serve at love to claim victory after 75 minutes, taking her fifth triumph in six career matches against the Russian.
"I'm always so on edge when I'm playing her, like at the end," Pegula said. "She hits a couple winners, and I miss a couple balls and all of a sudden it's 5-all.
"It felt like it was straightforward, but at the same time in my mind it didn't feel like it."
Pegula will play against fourth seed Diana Shnaider, who ousted Russian compatriot Liudmila Samsonova 6-3, 6-4.
Japan's third-seeded Osaka, a four-time Grand Slam winner, rallied to eliminate Italy's Elisabetta Cocciaretto 4-6, 6-4, 6-3 after two hours and 11 minutes.
World number 13 Osaka next faces either Ukraine's second-seeded Elina Svitolina or Alexandra Eala of the Philippines.
"In the first set, I had low energy, and I kept trying to pump myself up, but something was a little flat," Osaka said. "In the second, I just wanted to give it my best shot even though I wasn't playing too good."
Other later men's quarter-finals pit American Ben Shelton, the world number eight, against Chile's Alejandro Tabilo and Italy's 15th-ranked Lorenzo Musetti against 24th-ranked Spanish teen Rafael Jodar.