Neither player dropped a set in the quarter-finals, with Nakashima beating Italy's Luciano Darderi 6-2 6-3, before Jodar defeated France's Arthur Fils 7-6 (7-5) 6-3 on Tuesday (local time).
Nakashima sent down 11 aces and offered up a subdued celebration for the career-breakthrough win in Montreal.
He will meet Jodar for a place in the final after the Spaniard extended his breakthrough season with a 34th win of the year.
The 28th-seeded Nakashima converted a break point in the fourth game before breaking his opponent to love to close out the first set, as the visibly frustrated Darderi's composure unravelled.
Darderi dug in his heels in the second set but could only hold off the determined Nakashima for so long, as the American broke him on the fourth try in the penultimate game.
Nakashima sent 19th-seed Darderi skittering around the court in the final game, forcing him into an error at the net on match point and pumping his fists in celebration after the customary post-match handshake.
In the other quarter-final, Jodar extended his remarkable first season on tour with a composed win over Fils.
He earned an early break, but Fils fought back before rain suspended play again with the Frenchman serving to stay in the first set.
Jodar took the opener in a tiebreak after the restart and carried his momentum into the second set, breaking three more times to secure the victory that will lift him to at least No.11 in the rankings.
"I played a very high level against a tough player like Arthur," Jodar said in his post-match on-court interview.
"I had to give my best to win this match. It worked perfectly, staying calm in those important moments of the match, those pressure moments."
The US Open tune-up tournament was without several top players, including world No.1 Jannik Sinner and 24-time grand slam champion Novak Djokovic, which the Professional Tennis Players Association this week blamed on players' workload.
The men's quarter-finals began a day late after inclement weather forced the postponement of the Monday program.
- with PA
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