Joel Peralta came in to pitch and Olivo greeted him with a blast to left field that landed in the bullpen, handing the Mariners their third victory in four games against the Rays and their sixth straight series win.
Bradon League racked up his 16th save and Jamey Wright (2-2) got credit for the victory, despite allowing the Rays to score three runs in the top of the eighth to tie the score.
Greg Halman went 3-for-4 with two RBI and Ichiro Suzuki also drove in two with a pair of hits for Seattle, which wrapped up a 7-3 homestand.
Ben Zobrist and Kelly Shoppach each had two hits and a run driven in for Tampa Bay.
Notable deaths of 2014 [PHOTOS]