Thiem, who was celebrating his 27th birthday on Thursday, comprehensively defeated Nagal 6-3, 6-3, 6-2 in two hours in Arthur Ashe Stadium.
The 23-year-old Indian threatened early in the first set, levelling the scoreline after being down 0-3. It brought back memories of when he stole the opening set against Swiss legend Roger Federer in the first round contest during his US Open debut last year. But the second-seeded Austrian put his foot on the gas pedal to reel off the next three games, taking the set and denying Nagal a chance to recreate that 2019 scenario.
Thiem's dominance continued as he broke Nagal at love to end the second set, and the Austrian's momentum never slowed the rest of the way. Nagal fought through to the very end, but a volley that sailed long handed Thiem the victory.
"Thank you 2020 US Open. Lots to learn. Going to keep working hard! Thanks for all the support everyone," said Nagal in a tweet after the defeat.
During the course of the match, Thiem converted on 6 of 14 breakpoint chances and finished with 30 winners while Nagal fired 12 winners and committed 38 unforced errors.
Qualifies into the main draw last year. Makes it to Round 2 this year.Sumit Nagal always leaves it all on the court.@NagalSumit I #USOpen pic.twitter.com/uyk054v3zl— US Open Tennis (@usopen) September 3, 2020
"I think it's going in the right direction," Thiem said after the match. "It's difficult to say where I stand, I've been playing a lot of exhibition matches while we were away, but it's not the same as here, where it's more serious. I would like to get back to where I was before we stopped playing."
Thiem will now face 2014 champion and No. 31 seed Marin Cilic.