Birthday boy Thiem, who turned 27 was a little rusty in the first round, won the contest 6-3, 6-3, 6-2 against Nagal to move into the third round of the US Open.
Up next for Thiem, who was runner-up at the Australian Open this year, is 2014 champion Marin Cilic of Croatia who beat Slovakia’s Norbert Gombos 6-3 1-6 7-6(2) 7-5.
"He is a real champion, one of the very few active Grand Slam champions. He knows what it takes to win big matches. It's going to be tough," Thiem said of his next opponent.
Nagal became the first Indian to win a singles match at the US Open in seven years after Somdev Devvarman (2013) when he beat Bradley Klahn. After taking a set off Roger Federer in his outing at the US Open last year, Nagal has gone one better this time – a second round appearance.