Fritz needed three sets to get past Norrie in the evening match as the 21-year-old American continued his bid for a second career title after capturing his first at last month's Eastbourne International.
It initially looked like it would a short contest as Fritz's pinpoint serving befuddled Norrie but the Briton bounced back in the second to force a decider.
Fritz seized the momentum in the third when he hammered a crosscourt forehand winner to give himself a break point opportunity and converted it when Norrie sent a forehand long to fall behind 4-2.
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The best rally of the match came on match point when the players exchanged volleys at the net before Fritz's final effort flew past Norrie and caught the back line to seal the win.
"I was really happy with my ability to turn it around after losing the second set," Fritz said.
"I tried to make a couple adjustments in the third, I won a lot of important points and was mentally able to turn it around."
Fritz will take on Alex de Minaur, who outlasted big-serving Reilly Opelka 7-6(4) 6-7(5) 6-3 in Saturday's earlier match.
Despite the towering Opelka pounding down 28 aces it was De Minaur who had the better serving in their semi-final on a hot and humid day in Georgia's capital city.
The Australian won 96 percent of his first-service points and never gave Opelka a break point opportunity.
The turning point came in the third set when De Minaur finally broke Opelka's serve to go up 3-2.
The 20-year-old broke again on match point when Opelka sent a backhand into the net for his 38th unforced error.
"Reilly is an incredible competitor, a super tough guy to play and a great friend," De Minaur said in a courtside interview.
"It's a bit of a lottery out here. I just had to guess the right way [when returning] on a couple [of] big points and I was fortunate to get the win today."
De Minaur will play in his fifth career ATP final on Sunday with his lone title coming earlier this year on home soil at the Sydney International.
Despite the loss, Opelka will enter the top 50 for the first time in his career when the new rankings are released on Monday.
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