Jennings drove in the winning run with a two-out single in the bottom of the ninth inning in a 7-6 victory over the Miami Marlins on Tuesday.
It was the sixth game the Rays have won this season after giving up six runs or more, matching last season's total. The Rays finished with 16 hits.
"It's so much fun to watch right now," Rays manager Joe Maddon said. "Even when we were down early and their pitcher was pitching well, I just felt confident that we could come back."
The Rays overcame an early 4-0 deficit and won their third in a row. Miami lost its seventh straight game.
With two outs Jennings, who was recently dropped from first to seventh in the Tampa Bay batting order, singled sharply down the right-field line against Chad Qualls, Jennings' third hit of the game.
"I felt I had good at-bats all night," Jennings said. "I remember Joe (moved me down in the batting order) last year toward the middle of the season. It always seems to work."
Fernando Rodney (2-2) got the win.
Chris Coghlan homered, tripled and drove in three runs for the Marlins. Miami scored five or more runs in a second straight game for the first time this season.
"Anytime you get walked off three times in a road trip, that's rough," manager Mike Redmond said after the Marlins' winless trip. "It wears on everybody. Guys are battling. They're out there playing hard. I sensed that the attitude was good in the dugout. Guys are trying. We just didn't get it done."
Coghlan led off the sixth with his first home run of the season.
Hellickson pitched 5 1/3 innings, giving up five runs and seven hits.
"You're disappointed anytime your team gives you the lead and you can't hold on to it," said Slowey, who gave up four runs and eight hits. "I thought tonight was a battle on both sides, for both pitchers, both bullpens and all the way around."
Johnson doubled home a run in the third. He has 25 RBIs in 22 games this month.
The Rays optioned LHP Jake Odorizzi to Triple-A Durham. They will call up another pitcher Wednesday to start Saturday's game at Cleveland. ... Rays LHP David Price threw for a second straight day, but the AL Cy Young Award winner will miss a third start since straining his left triceps on May 15. The Rays have made no announcement indicating Price will be taken off the DL when he becomes eligible Friday. ... Marlins INFs Joe Mahoney (right hamstring strain) and Donovan Solano (left intercostal strain) are expected to start playing in minor league games by the end of the week. RHP Nathan Eovaldi (right shoulder inflammation) could be ready to return after two more minor league starts.