Sweeting, ranked 119th in the world, downed his fellow American 3-6, 6-3, 6-4.
Blake, who won the tournament in 2002 and was runner up in 2005, had won his first matches in four years last week. His comeback attempt was derailed Tuesday, however, when he lost three break points in the first set and failed in four opportunities to break Sweeting's serve in the decisive set.
"I just wasn't doing the things I needed to do to win matches," said Blake, who was sidelined with a knee injury earlier this year. "I played tentative on the big points; I needed to step up to take control of the big points."
Argentina's David Nalbandian advanced along with Sweeting to the second round by dispatching Rajeev Ram of the United States 6-4, 6-0. Nalbandian, a former world No. 3, is coming back from a hip injury that sidelined him much of last year.
2014: The Year in Music [PHOTOS]