Reid Brignac drove in three runs to back 1, in the rubber match of a three-game series.
The 24-year-old Hellickson (12-10) gave up one run on four hits. The right- hander only struck out one batter, but got 16 groundouts.
"I knew they were swinging early," Hellickson said. "I didn't know my pitch count was that low. I just kept attacking the zone and they kept putting it in play."
Adam Jones hit a solo homer for the O's, who have lost six of eight. Jones also hit a double in defeat.
Jeremy Guthrie (6-17) got blasted to the tune of seven runs -- three earned -- on seven hits over five innings. He struck out five and walked four.
"My main goal coming into the year was hopefully to win double-digit games for us," Guthrie said. "As it stands, I got four more chances to win four games, and that would put me at 10 which is a small accomplishment for the season. That's what I've been shooting for."
The Rays got to Guthrie early and often. With one out in the second inning, Brandon Guyer reached base on an infield single. Two batters later, Rodriguez hit a homer over the wall in left for an early 2-0 lead.
Tampa Bay pushed across four more runs in the third to create some distance. Evan Longoria and Joyce walked with one out. Runners were at the corners after Jose Lobaton grounded into a fielder's choice. Casey Kotchman walked to load the bases. A run scored when Guyer reached first on third baseman Mark Reynolds' fielding error. Brignac then cleared the bases with a double to left-center field to make it 6-0.
Joyce's sacrifice fly in the fourth made it a 7-0 contest.
Baltimore's first hit of the game didn't come until the fifth, when Jones led off the frame with a homer to left.
Joyce's solo homer off Rick VandenHurk in the sixth extended Tampa Bay's margin to 8-1.
The Rays have taken eight of 15 games from the O's this season...Hellickson did not walk anyone and threw 67 of his 97 pitches for strikes. He improved to 4-1 lifetime against the Orioles...Guthrie fell to 6-10 in his career against Tampa Bay...Baltimore left fielder Kyle Hudson went 0-for-3 in his MLB debut...VandenHurk gave up one run on one hit over 2 1/3 innings.