Darcis, who made it to the third round of the London Olympics, outlasted fifth-seeded Roddick in a pair of tiebreak sets, 7-6 (8/6), 7-6 (7/3) at the Wake Forest University facility.
The 28-year-old Darcis, who is ranked 81st in the world, was the last player to make the cut for the main draw.
Roddick, a former world No 1 and ex-US Open champion, is struggling heading into the last Grand Slam of the year at Flushing Meadows.
“I served okay, but I didn’t return too well,” said Roddick. “I didn’t hit the ball clean and he played better when he had to. I wanted to play better here.”