Machac made a promising start to Saturday's match by winning the opening two games before Sinner got on the board, with the top-seeded Italian closing out a hard-fought first set in 44 minutes after errors flew from Machac's racket.
The twice grand slam champion was made to work hard by Machac, even more so in the second set, but Sinner proved too solid for his fellow 23-year-old as he sealed his 64th win of the year while making just nine unforced errors.
Sinner will next face fourth-seeded record 24-times major winner Novak Djokovic or American seventh-seed Taylor Fritz, who play in the second semi-final later on Saturday.
The Italian's dominant season has brought him his maiden slam at the Australian Open and another at the US Open.
"It's amazing. It's something you dream of when you're a kid, when you're young. Just to reach the number one spot, now but to have the year-end ranking ... it's also a different and special feeling," Sinner said.
"But this happened during the tournament. So I'm not even thinking about that. I know tomorrow will be an important day ... but it means so much to me obviously."
Machac, who won the mixed doubles gold medal at the Paris Olympics, had ended Carlos Alcaraz's 12-match winning streak to reach the last four.
"I think we all saw how much talent and firepower he (Machac) has," Sinner said. "I had to be very, very careful in every service game. He's returning very aggressively and very fast."
Sinner can win his seventh trophy of the year on Sunday.
