Fritz had 22 aces in his 7-6 (7-5) 7-6 (7-3) victory, while Shelton sparked his game with a scintillating crosscourt forehand winner while facing three break points early in the second set and going on to a 4-6 6-4 7-6 (7-4) win.
The 28-year-old Fritz is ranked seventh in the world, two spots ahead of Shelton, who is coming off an Australian Open quarter-final appearance that ended with a loss to Jannik Sinner in straight sets.
Fritz, a 10-time ATP Tour champion, and Shelton split their first two meetings.
Shelton has three tour titles heading into the final on Sunday (Monday AEDT).
"Are you guys telling me that's the final you want to see?" Shelton asked, prompting cheers from fans at the indoor football stadium that is also a practice field for the Dallas Cowboys at club headquarters.
"I'm super-excited for that match-up."
Shelton came back from a set down for the second consecutive match, after beating Miomir Kecmanovic in the quarterfinals.
The 23-year-old was down a set and facing three break points at 1-1 in the second when the crosscourt winner got him going. He later had two set points on the seventh-seeded Shapovalov's serve, and converted the second to force the deciding set.
Shelton won three of the last four points in the tiebreaker, clinching the victory with another forehand winner.
Fritz had three set points in the first tiebreaker and three match points in the second against the unseeded Cilic.
The 2024 US Open finalist closed out the first with his third consecutive ace after Cilic saved two set points.
