In his fourth start of the season, Hellickson (1-1) limited the A's to one run on two hits with three strikeouts over seven strong innings.
The right-hander, who sat out the first three-plus months of the season recovering from arthroscopic surgery on his pitching elbow, was the winning pitcher in an 18-inning affair against Baltimore on Sept. 20 and hadn't won a game he started since Sept. 4 against the Angels.
Kevin Kiermaier homered and drove in three, Desmond Jennings knocked in a pair and Ben Zobrist went 3-for-4 with an RBI and a run scored for Tampa, which salvaged the final game of the series after mustering two runs in the previous two games.
The Rays had lost three straight and five of their last six coming in.
Sonny Gray (12-5) was roughed up for season highs of seven runs -- six earned -- and 10 hits in 4 1/3 innings on the hill.
Josh Reddick had two RBI and Eric Sogard cracked his first homer of the season in the setback.
Tampa Bay manufactured the first run of the game with a couple of base hits in the second. Yunel Escobar singled to begin the frame, then advanced to second when Cole Figueroa reached on an infield single after executing a hit-and-run. Jose Molina moved the two runners into scoring position with a sacrifice bunt and Kiermaier knocked in Escobar with an RBI groundout.
Gray walked three of the first four batters he faced in the third, but the reigning AL Pitcher of the Month worked out of trouble, getting Escobar to ground into a force out at home and Figueroa to fly out to right.
Jose Molina legged out an infield single in the fourth before Kiermaier knocked his ninth homer of the season to give the visitors a three-run cushion. Zobrist hustled for a double later in the inning and scored on Evan Longoria's bloop single to center.
Hellickson allowed a base hit to Coco Crisp to open the fourth which was the first baserunner for Oakland on the day. The right-hander worked around the leadoff man, though, inducing a lineout of John Jaso before fanning Josh Donaldson and Brandon Moss to end the inning.
Tampa Bay opened up the margin in the fifth and chased Gray from the contest in the process. Escobar slapped a single to left and advanced to third on Sogard's error that could have possibly been the start of a double play.
Kiermaier was hit by a pitch two batters later to load the bases which preceded Jennings' two-run single. Zobrist followed with a run-scoring hit to right.
Sogard got a run back in the sixth with a solo homer down the right-field line.
With two outs in the ninth, Donaldson singled and Moss walked to set up Reddick's two-run double which accounted for the final margin.