Musetti lost only three points on serve to beat Poland's Daniel Michalski 6-1, 6-1 in just 57 minutes in the best-of-five-match Brisbane city final.
The winners of the city finals in Brisbane, Sydney and Perth progress to the semi-finals of the inaugural mixed teams tournament along with the best-performing losing finalist.
The 20-year-old Musetti, who climbed to 23 in the world in 2022, had far too much firepower for his opponent, blasting 17 winners past the 260th-ranked Michalski.
"I was so focused today on the match and the serve was really good," he said. "But with every shot I had a great feeling for the ball so I think I played the best match so far."
However, Poland struck back when Swiatek battled past Trevisan 6-2, 6-4.
The three-time Grand Slam winner raced through the first set but was forced into a fight in the second, finally claiming victory in one hour and 51 minutes.
"It became tight at the end and I felt like she had her chances as well," Swiatek said. "My goal is to be more consistent and keep the same level of tennis right to the end."
In Sydney, a tenacious Madison Keys gave the United States an early lead over Britain before Cameron Norrie struck back when he won a high-quality match against Taylor Fritz in their city final.
World number 11 Keys lost the first set to Katie Swan before recovering to win a gruelling match 2-6, 6-3, 6-4 in two hours and 18 minutes.
"I actually practised with Katie a few days before the tournament and I said to my coach she's playing absolutely great tennis," Keys said.
"So I knew I would have to play well and I think she played a phenomenal first set and I knew I had to raise my level."
Norrie and Fritz played an enthralling encounter which was in the balance until the Briton broke at 4-4 in the final set then served it out to claim a 6-4, 5-7, 6-4 victory.
"All credit to Taylor, we've played so many times and always had a battle so I was definitely ready for three sets," Norrie said.
Croatia took the first point in Perth when Donna Vekic downed Greece's Despina Papamichail 6-2, 6-0.
Stefanos Tsitsipas takes on Borna Coric in the second singles rubber.