Thiem broke the Grand Slam stranglehold of Roger Federer, Rafa Nadal and Novak Djokovic by winning the 2020 title in New York but a wrist injury the following year sidelined him for months and other niggles meant his ranking slipped to 352nd.
The Austrian, now ranked number 81, has endured a dismal run at the majors since reaching the Australian Open fourth round two years ago and said beating Bublik 6-3 6-2 6-4 felt special.
"Yeah, it was a very good match basically from the first moment on. It's a pretty special victory, because it's the first since 2-1/2 years in Grand Slams," Thiem told reporters.
"I think, I don't know, six or seven Grand Slams without a match win. So it's great. Especially here at the US Open with all the past and all the memories I have here."
Thiem said he had slowly regained full strength in his wrist but rediscovering his confidence proved to be a challenge after his return in March 2022.
"The physical trust is there. Since the injury I've played many tournaments. I did many practice sessions. I really also gave a lot of load on the wrist again. It's completely fine," said Thiem, who meets American Ben Shelton next.
"The mental side wasn't easy to restore. Wasn't doing the same job I was used to before the injury, that wasn't easy.
"With every success, every match, especially with bigger successes or better weeks like I had in Austria when I played my first finals or also here ... it helps a lot on the mental side and to get full trust again in the wrist."
