The Austrian celebrated turning 27 by defeating India's Sumit Nagal 6-3, 6-3, 6-2 inside an empty Arthur Ashe Stadium.
"I was trying to play my fastest tennis to keep him on the backhand, to not let him dictate with the forehand. I did that very well today," said Thiem.
The world number three will play 2014 US Open champion Marin Cilic in round three.
"He's one of the big champions of the last decade, one of the very few players, active players, who won a Grand Slam tournament here in New York," said Thiem.
"Even though for sure he's not on the top of his game, beginning of this year, maybe also last year, he's always dangerous for a big and deep run in these big tournaments.
"It's not a guy I want to face in the third round," he added.
Thiem said it was difficult playing in front of empty stands at the US National Tennis Center because of the coronavirus pandemic.
"In negative moments the fans' energy can get you up again. Now you play a great point and it's complete silence. That is tough.
"Hopefully this is the only or one of very few slams where we have the situation like that," Thiem added.
Cilic, seeded 31st, took four sets to overcome Slovakian Norbert Gombos 6-3, 1-6, 7-6, 7-5.
Nagal had become the first Indian man since 2013 to reach the second round of a Grand Slam.