Former world number one Roddick claimed the first 6-7 but his opponent hit back 7-5 6-1 to advance to the second record in Ohio.
"I was just disappointed," said the 28-year-old after the match. "Equal parts mad and disappointed in myself.
"My team also, we've been trying hard to get back. It's essentially a long uphill battle."
American Roddick is currently ranked number 12 in the world.