Jeremy Guthrie got no run support, again.
Guthrie (1-6) gave up seven hits in his first complete game of the season, but fell to 0-6 in his last seven starts since beating the Rays on opening day. The Orioles have scored six runs over the seven-start stretch — including no runs five times — while he was in the game.
"Timing is everything with something like that," Orioles manager Buck Showalter said. "He certainly doesn't want to hear it right now, I can tell you that."
Joyce put the Rays up with a two-run homer off Guthrie in the second inning. He had two hits and is 23 for 48 with five homers and 13 RBIs over his last 14 games.
"There wasn't much margin for error," Showalter said. "We got four hits."
Damon made it 3-0 with a homer in the eighth inning. He broke a tie for 73rd place on the career hits list with Tim Raines and Rabbit Maranville with his 2,606th hit.
Guthrie has given up two homers in each of his last three starts. In the previous two outings, Baltimore had not scored when he departed.
"We know it's difficult," Showalter said. "We've talked about it. He won't give in."
Baltimore was bidding for its second four-game winning streak this season.
Hellickson (4-2) struck out three and walked one in his first career complete game. The right-hander retired his final 13 hitters.
"I felt just as good in the ninth as I did in the first," Hellickson said.
The Rays improved to 10-10 at home this season and Tampa Bay is 13-5 on the road.
"Hellickson, obviously, was in command," Showalter said. "Didn't have many good at-bats off of him."
Guthrie has lost two of three starts this season against Tampa Bay, including an 8-2 defeat to Hellickson last Saturday. Hellickson allowed three hits and five walks over five shutout innings in the game.
The complete game was Guthrie's third overall, and first since May 3, 2009, against Toronto.
It was the third time ever at Tropicana Field that both starters had complete games. The other two took place in 1999 and 2003.
Notes: Orioles slugger Vladimir Guerrero had the day off. ... Tampa Bay CF B.J. Upton served the second game of a two-game suspension handed down by Major League Baseball following a tirade after he was ejected on May 4. ... Orioles LHP Brian Matusz, who has been on the DL all season because of a strained ribcage muscle, had a 45-pitch bullpen session. He is scheduled to start for Class-A Frederick on Monday. ... Rays LHP J.P. Howell (left shoulder surgery) could rejoin the team next Thursday. The reliever is on a rehab assignment at Triple-A Durham. ... Baltimore RHP Justin Duchscherer (left hip) threw two innings at extended spring training.