Hellickson (7-3) reeled off a fifth victory in six June starts, during which he has posted an ERA of 1.42. The right-hander yielded one run on six hits over six full innings, walking thee and striking out six.
Jake McGee, Kyle Farnsworth and Joel Peralta teamed up for two scoreless relief frames and Fernando Rodney closed out the victory with his 17th save as Tampa Bay took the rubber match of a three-game series.
Jose Lobaton led the Rays' offense, going 3-for-3 with a pair of run-scoring singles.
Detroit's Rick Porcello (4-6) absorbed the loss, yielding three runs on eight hits over six full frames.
Miguel Cabrera socked his 25th homer of the year for the Tigers, who fell into a first-place tie with Cleveland atop the American League Central.