Jodar, 19, had been hoping to make history in the Montreal for the fastest rise into the top 10 of men's tennis but his attempt to make a first Masters 1000 final was ended in straight sets by American Nakashima.
Nakashima, the 28th seed, had never previously made it past the third round at the tournament but was too strong for Jodar in a 7-6 (7-3), 6-4 triumph.
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Jodar saved four match points before Nakashima finally converted his fifth to overcome the world No 15 in two hours and two minutes of play on IGA Stadium.
"Going into the tournament, I knew I was playing at a really high level, so I knew that I could get a go on a deep run here," said Nakashima.
"Obviously, wasn't thinking about the final or anything."
Nakashima will face defending champion Ben Shelton in an all-American final on Friday, live on Sky Sports Tennis.
Shelton beat compatriot Learner Tien in the night's second semi-final and said afterwards: "Super happy with the performance.
"Learner is a guy who presents me with a lot of problems in my game. A tough challenge to overcome.
"To get a win over him in the fashion that I did, I'm super pleased with that."
Rybakina fights back to beat Gauff to set up Swiatek final
At the women's semi-finals in Toronto, second-seeded Elena Rybakina beat fourth-seeded Coco Gauff 5-7, 6-2, 6-2 to book her place in the final.
Rybakina will play seventh-seeded Iga Swiatek on Thursday night after the Pole saw off ninth-seeded Elina Svitolina 6-3, 1-6, 6-3.
The 6ft Rybakina finished off Gauff just before 1am local time to bring the rain-delayed night session to a close. The Kazakh has won the Australian Open and Stuttgart titles this year, taking her career tally to 13 titles.
In the first semi-final, Swiatek broke Svitolina's serve at love for a 5-3 lead in the third set. Swiatek then jumped out to a 40-0 lead before converting her second match point. The match began about an hour after the scheduled start because of rain.
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