Thiem reached his first Tour-level semi-final in more than a year at last month's Swiss Open, a key milestone as he works to regain his form after a June 2021 wrist injury, but showed he still has work to do as he stumbled into 30 forehand unforced errors on Court 17.
Carreno-Busta, fresh off his maiden Masters 1000 title in Montreal, overcame early jitters that saw him drop his serve in the first game to put up a comparatively clean performance, winning nearly two-thirds of his first-serve points a year after he crashed out in the opening round.
He next faces Kazakhstan's Alexander Bublik in the US Open second round.