Sinner will face either Novak Djokovic -- a four-time Shanghai champion -- or world number seven Taylor Fritz in the final on Sunday.
The 23-year-old has been in top spot since June and after his ruthless semi-final victory will stay there until at least the end of the season, the first Italian to do so.
"It was only a dream just to become number one... Now finishing (the year there) is also a different feeling," the Italian said.
"It's a good feeling. I'm very happy to achieve this. It was an amazing season for me and it's not finished yet," he said, adding that for now he was "focused on tomorrow".
Sinner's meeting with Machac got off to an electric start when the Czech broke in the first game of their semi-final.
The 33rd-ranked Machac was looking to repeat his giant-slaying of Thursday, when he knocked out world number two Carlos Alcaraz in straight sets.
But two-time Grand Slam champion Sinner kept his cool to break back in the fourth, then claimed the tenth game to clinch the set.
In the second set neither was able to break serve until the 12th game, when the Italian hit a winner to book his place in Sunday's final.
"It was very tough... he is playing with so much confidence and he can hit a ball really hard, and is serving very well," said Sinner.
"I tried to stay there mentally... I'm very happy about how I'm fighting at the moment."
