The red-hot Americans made a strong start to the semi-final having gone ahead 2-0 on Friday after Jessica Pegula and Frances Tiafoe scored convincing victories and world number nine Fritz held his nerve to finish the job against Hurkacz.
The Indian Wells champion Fritz saved two set points while down 5-4 in the opening set as Hurkacz faltered and the American took the lead in the match when his opponent made another error at the end of a tight tiebreak.
Fritz, who won 88% of his first-serve points, needed a big serve to hold for 6-5 in the second set before claiming the win in another tense tiebreak to send his side through to a title clash with either Italy or Greece.
"It was great to get the win today to get us through. I had no doubt that if I were to lose that the rest of the team would have come through," Fritz said.
"But I've played with Team US a lot. I think it's a huge advantage this time having the girls on our team because it just makes the whole team so much stronger.
"I'm super excited going into the final and I think we've been the favourites all week."
Madison Keys then beat Magda Linette 6-4 6-2 to make it 4-0 before Fritz and Pegula rallied from a set down to win the mixed doubles rubber against Lukasz Kubot and Alicja Rosolska 6-7(5) 6-4 10-6 for a clean sweep.
Italy came into their clash with Greece holding a 2-0 lead after Martina Trevisan and Lorenzo Musetti won their matches but Stefanos Tsitsipas reduced the deficit with a thrilling 4-6 7-6(2) 6-4 win over Matteo Berrettini.
In a high-octane match played in front of predominantly Greek supporters at Ken Rosewall Arena, Tsitsipas looked set for defeat as Berrettini dominated the early proceedings on the back of his booming serve and thunderous forehand.
But Tsitsipas flipped the script, edging the second set by forcing Berrettini into making uncharacteristic errors from the baseline. The world number four recovered after being broken in the decider to quell Berrettini and spark wild celebrations.
Lucia Bronzetti ensured there was no late comeback by getting past Valentini Grammatikopoulou 6-2 6-3 to send Italy into Sunday's final in Sydney.
