Sheets signed a one-year, $10 million contract with Oakland after missing last season with elbow problems that required surgery. He gave up eight hits and a walk, and another batter reached on an error.
Chris Dickerson ended Sheets' day with a two-run homer in his second at-bat of the first inning. Sheets has allowed 18 runs in 4 1/3 innings over his first three spring outings.
One of the hits came off a comeback grounder that bounced off Sheets' glove, keeping the rally going.
"It was a bad one," Sheets said. "I could have at least got an out if I could catch the ball. I don't care whether they called it a hit or an error. It was hit right to me.
"I felt great," he said. "The problem is my good pitches were just a strike and my bad ones were hits. You need your good pitches to be put in play. That's how you get outs. When you can't even get out of the first inning, it's ridiculous."
Sheets gave up six runs against the White Sox on March 10, a game he still considers his low point of spring training.
"The second start [against Chicago], I felt worse," Sheets said. "I felt terrible. This start was probably the best. I threw 91 mph, which is reasonable. I want to be successful. The lights are going to come on as long as I'm feeling OK."
Manager Bob Geren saw progress in Sheets' outing.
"He definitely threw the ball better this time," Geren said. "The results weren't there. It's the best he's thrown since he's been here. I'll stay encouraged that way. This guy's an All-Star. He didn't like his performance. I'm not worried about his ego."
Mike Lincoln, who is competing for the fifth spot in Cincinnati's rotation, retired the first six batters before giving up four runs in the third.
"I felt good today," said Lincoln, who had neck surgery last year. "I stayed nice and loose even after that long inning. That last inning I still felt good."
Dickerson, who is competing for the starting job in left with Jonny Gomes, also had a double off Sheets and went 4 for 4, raising his batting average to .429.
"Hey, man, that's how you do it," manager Dusty Baker said. "The thing about it is you go play your way into it. You don't talk your way into it."
Oakland RHP Jason Jennings changed his number from 77 to 29 for the rest of spring training. ... Oakland pitching prospect Travis Wood threw three innings, allowing one run. It's the only run he has given up in seven innings. Wood had a 1.21 ERA in the Southern League last season. ... Gomes also had a pair of hits, raising his average to .333.