Tampa Bay won the final two games of the series, getting four RBI from Longoria and a one-run performance over 3 1/2 innings from its relief corps.
The game was deadlocked at 3-3 through four innings.
Jennings hit a solo homer off starter Henderson Alvarez (0-2) in the fifth and Longoria produced a two-run blast later in the inning. Longoria also had an RBI single in the first and an RBI double during the Rays' three-run ninth.
Jeremy Hellickson (2-0) gave up three runs, two earned, on six hits over 5 2/3 to get the victory.