Fritz, the world number 12, won 4-6, 7-5, 4-6, 6-4, 6-1 and will take on top-ranked Jannik Sinner for the title on Sunday.
"He overwhelmed me at the start and I was freaking out a little," said 26-year-old Fritz after securing victory with a 16th ace.
"I just told myself to stay in it, hold serve and apply scoreboard pressure.
"I did all I could to stay in it. If I hadn't have done that I'd regret it forever. In the final, I will come out and give it everything."
Australian Open champion Sinner earlier became the first Italian man to make the New York final with a 7-5, 7-6 (7/3), 6-2 win over Britain's Jack Draper.
Andy Roddick was the last American to make a men's singles final at the Slams at Wimbledon in 2009. He was also the last man from the country to capture a Slam title when he won the 2003 US Open.
Tiafoe went into Friday's match trailing 6-1 in his head-to-head record against his compatriot.
However, he boasted the more impressive Grand Slam credentials, playing in his second US Open semi-final in his last three appearances.
Fritz was in unknown territory, having fallen at the quarter-final stage at the Slams on four occasions.
Tiafoe used that greater experience to hit back from 3-0 in the first set to clinch the opener.
Fritz, who had reached the semi-final by defeating fourth-ranked Alexander Zverev in the previous round, was unable to convert a set point in the 10th game of the second set.
He succeeded at the next time of asking to level the match before handing the initiative straight back when Tiafoe broke for 1-0 in the third and held the advantage to retake the lead.
In a match where there were few rallies and little real drama, Fritz levelled again in the 10th game of the fourth set when Tiafoe dumped a lazy drop shot into the net.
That suddenly drained the spirit from Tiafoe as Fritz raced to victory in a brutally one-sided decider in which his opponent managed just nine points.
