Tampa Bay trailed 6-5 in the eighth but forged a tie when Yunel Escobar delivered a two-out, run-scoring single against Mike Dunn (1-1).
Then in the ninth, Johnson led off with an infield hit and Evan Longoria singled him to second.
Two outs later, Chad Qualls took the mound and Jennings (3-for-4) greeted him by ripping an opposite-field hit to right for the walk-off winner.
Fernando Rodney (2-2) earned the decision with a 1-2-3 top of the ninth for the Rays, who won a second straight in their four-game, home-and-home interleague rivalry series with the Marlins.
Scott finished with three hits and Jose Lobaton stroked a two-run double in the victory.
Chris Coghlan smacked a solo homer and added a two-run triple for Miami.
Celebrity Families of 2014 [PHOTOS]