With the win, the Rays snapped a two-game losing streak and moved to 35-29 on the season, four games behind the American League East-leading Red Sox.
Trailing, 1-0, after the top of the first, Tampa Bay answered in the bottom half of the inning when Jon Lester walked James Loney with the bases loaded to force home Jennings.
"The first inning sums up the whole night -- not able to repeat whatever pitch it may be -- fastball, curveball, changeup, cutter," said Lester, who threw 26 pitches in the first inning, of which just nine were strikes. "Just was not able to repeat. Whether it be the location or the pitch in itself, it's not good."
In the second, Jennings added a solo home run, the first of two he'd hit in the game, as he made a glorious return to the leadoff spot after 13 games of batting lower in the order.
By the time all was said and done, the Rays hit four homers. Evan Longoria hit his 12th, a solo shot, in the fourth and Matt Joyce added a two-run homer in the fifth, giving him 12 for the season.
"Properly struck," manager Joe Maddon said. "Desmond, both of them were really crushed, and I think Matty's was in the last row. He really hit that well. And then, of course, Longo goes to the opposite field, which was nice. I've talked about it, even back in Spring Training, that everybody discounts our power. We have power. And it's really nice to see it coming through."
The home run outburst came after the Rays hit four in Monday night's game, giving them their first back-to-back four-homer games.
Hernandez put forth an inspired effort in his 12th start of the season on a night when the Rays badly needed him to pitch late into the game.
The Rays used eight pitchers on Monday and had infielder Ryan Roberts warming up in the bullpen had the game gone to a 15th inning. Hernandez's performance brought soothing relief, as he went seven-plus innings, holding the Red Sox to three runs on seven hits to earn his fourth win of the season.
"I'm very happy," Hernandez said. "I'm confident with every pitch and throwing [them] for strikes. [I had] a little bit of trouble in the first inning with the ball not moving down. After that I kept the ball down and made good pitches. … I [didn't] try to overthrow, just kept the ball down. In the first inning, I tried too hard, and the ball didn't move."
In that first inning, Hernandez appeared as though he might be in for a long night when he surrendered a run on two hits and two stolen bases.
"Roberto took charge, kind of not really sharp in the beginning, but I think I'm learning a lesson with him -- if we can get him deeper into the game, he gets better," Maddon said.
Hernandez threw a career-high 122 pitches after not reaching 100 in any of his previous five starts.
"Such a strong guy, his pitch counts coming into this game were relatively low," Maddon said. "So I felt good about him going deep into that game. Of course, the bullpen needed some rest, but I saw that he got better … and the swings weren't as good. So I kind of liked that whole thing. So hopefully, we all learned a lesson from that game tonight."
Heading into Wednesday's rubber game, the Rays trail the season series, having lost seven of nine games.
"We've got one more game tomorrow," Maddon said. "If we could actually 'Meat Loaf' them, that would be kind of nice before they leave town. They've kind of had their way with us to this point. And so to get that game tomorrow would be very nice."