The world number two eased past the 31st-ranked Czech 6-1, 6-4 to set up a second-round meeting with Alexei Popyrin in Doha, where Carlos Alcaraz is the top seed this week.
It was a convincing return to action for Sinner after his semi-final loss to Novak Djokovic at Melbourne Park last month. The Italian lost just six points across his nine service games.
Sinner raced through the first set in under half an hour but Machac improved in the second.
A break in the fifth game still proved enough for the four-time Grand Slam champion, although he needed five match points to close it out.