Shelton beat the French world number 47 5-7, 6-3, 6-4 in their last-four meeting.
Despite being a break up in the deciding set, Van Assche fell just short of the biggest win of his career and a first Masters final as Shelton showed his fighting spirit again.
It was a tournament to remember for the 22-year-old Van Assche, however, after eliminating former world number five Lorenzo Musetti and US 15th seed Learner Tien en route to the semi-finals.
In the first set, Shelton rarely looked comfortable and amassed errors on his usually solid groundstrokes.
The rot spread to his most formidable weapon, his serve, as Van Assche earned a break in the 11th game before holding to 15 to claim the frame in confident fashion.
The Atlanta native ended the set with 17 unforced errors, compared to just six from Van Assche.
"I made a significant amount of forehand unforced errors in the first set, and really my goal after that was to cut out those unforced errors, to be a little bit more solid, and to use the speed of the court to my advantage instead of fighting it," Shelton said.
His level slowly rose in the second set, and a whipped forehand passing shot at 15-40 allowed him to break Van Assche and move ahead 4-2.
With the set on his racquet, Shelton served it out to bring up a deciding set.
The nerves were palpable on court as two error-strewn games from both players produced consecutive breaks midway through the third set.
But once back on level terms, Shelton, the more experienced player in the later stages of tournaments with 10 final appearances, exchanged a relaxed high five with his father and coach Bryan after a backhand winner to hold, before breaking Van Assche in the next game to lead 4-3.
Shelton brought up two match points, securing his spot in the final at the second time of asking.
"It's tough out here," Shelton added. "The players are so good and it's not easy to close matches out."
The 24-year-old already holds two 1000-level titles, after winning the last two editions of the Canadian Open.
He'll meet either Carlos Alcaraz or former world number two Casper Ruud in Sunday's showpiece match.