Hellickson (4-0) allowed one run and five hits en route to winning a career-best sixth consecutive decision, dating to Sept. 4. The right-hander struck out six and walked two.
Tampa Bay second baseman Will Rhymes left in the eighth inning after being hit by a pitch near his right elbow. While standing at first base he gestured that he wanted to come out of the game, took a couple of steps and collapsed into the arms of first base coach George Hendrick. Trainers worked on Rhymes in the coach's box before he was assisted to a utility cart and left the field.
After Jake McGee and Joel Peralta both threw a scoreless inning, Fernando Rodney pitched the ninth for his 12th save.
Clay Buchholz (4-2) gave up two runs and six hits over five-plus innings for Boston. Buchholz, who took a grounder off his leg during the sixth, had allowed four or more runs in all seven of his previous starts this season.
Matt Joyce opened the sixth with an infield single that went off Buchholz's lower leg. He went to third on a single by Carlos Pena. Andrew Miller replaced Buchholz and gave up Scott's sacrifice fly that put Tampa Bay ahead 2-1.
The Rays, winners of four straight, loaded the bases with two outs later in the sixth, but Miller struck out Elliot Johnson on a 3-2 pitch.
Tampa Bay took a 1-0 lead in the second when Buchholz was called for a balk on a pickoff move to first with runners on the corners and two outs. Pena, who had a leadoff single, scored on the play. The Red Sox wound up with three balks overall.
Daniel Nava's fourth-inning RBI single got Boston even at 1-all.
Red Sox manager Bobby Valentine said left-hander Felix Doubront, who was hit on the ear by a ball during batting practice Tuesday, was cleared to make his start Thursday.
Meanwhile, Boston left-hander Rich Hill left the field after being struck by a ball in batting practice before Wednesday night's game. The team said Hill is OK.
NOTES: Red Sox closer Andrew Bailey (right thumb) is set to resume throwing next week. ... Boston 3B Kevin Youkilis (lower back) started a rehab assignment as the DH with Triple-A Pawtucket and could play in the field Friday. ... Valentine doesn't believe RHP Daisuke Matsuzaka (right elbow), scheduled to start for Pawtucket Thursday, is close to pitching in the majors. ... Rays 3B Evan Longoria (left hamstring) took batting practice, but has not started running. ... Red Sox LF Carl Crawford (left wrist) could start swinging a bat next week. ... The Rays acquired OF Rich Thompson from Philadelphia for minor league OF Kyle Hudson.