The Italian world number one needed just two hours and one minute to dispatch Popyrin 6-3, 6-2, 6-2.
Sinner – who only dropped four games in his first round win over Vit Kopriva on Tuesday – was similarly brisk against Popyrin.
The 24-year-old broke Popyrin five times as he moved through the gears against his opponent, ranked 36th in the world.
Sinner faces Canadian 27th seed Denis Shapovalov in the third round on Saturday.
“Obviously I try to play the best tennis I can, the first round match is always different compared to the further you go (in the tournament),” Sinner said.
“I’m very happy that I managed these matches as good as I could, when you are up two sets and a break you try to serve as best as you can.
“Today, it felt like neither of us served well but I was returning well and especially on the second serve. I am happy about today, I am aiming to improve on the serve but the rest (of my game) I am quite comfortable with.”
Sinner has reached the final of all three Grand Slams this season, winning the Australian Open and Wimbledon either side of a defeat to Carlos Alcaraz at the French Open.
He is bidding to become the first man to successfully defend the US Open since Roger Federer won the last of five consecutive titles in 2008. (AFP)