The day capped a massive weekend for both players. Longoria hit at least one homer in all four games against the Twins and had five during the weekend, establishing a franchise record for home runs in a series.
Morrison wasn't far behind, hitting at least one in each of the last three games and four overall.
Tampa Bay's 11 home runs as a team in a series also set a franchise mark.
"I mean both those guys, gosh, they're on fire," said Rays manager Kevin Cash. "Just shows when you get two really good really good hitters on fire, they can carry a big load for you offensively and they're doing that."
Longoria has hit safely in nine straight games and in 21 of the last 24 overall, slashing .344 with eight doubles, eight homers and 17 RBIs during that span.
"I altered my swing a little bit. I've widened out a little bit and it's really, I think, just enabled me to see the ball better," Longoria said. "It's kind of one of those moments where you realize that sometimes what you did early on in your career doesn't always work the whole time.
"It was a change that took place gradually, but now I feel like I'm in a really good spot. I'm just seeing the ball well and allowing myself to get into hitter's counts and taking advantage of those counts."
Minnesota hit three homers of its own, getting back-to-back solo shots from Byung Ho Park and Robbie Grossman in the third inning and a solo blast from Eduardo Nunez that tied the score at 5 in the bottom of the eighth.
The Rays scored two runs against Twins closer Kevin Jepsen to break the tie in the ninth, getting a leadoff double by Steven Souza Jr., who advanced to third on a fielding error. Jepsen sandwiched two walks around a strikeout before Brad Miller's sacrifice fly to left scored Souza. Longoria followed with an RBI single to give the Rays a two-run cushion.
"I know where I need to get to," Jepsen said. "Stuff-wise, it's coming, the velocity's coming. Mechanically, getting out there, I feel great as far as stuff's going. Now it's just putting it together."
Jepsen was charged with the loss, allowing two runs, two hits and two walks in two-thirds of an inning. Jepsen is 2-5 this year and saw his ERA jump to 6.26.
"He's a 95 mile-an-hour fastball guy but he needs that curve ball and changeup," Molitor said of Jepsen. "They haven't been there for him, at least reliably. He's trying to find that release point. I think that's probably the biggest thing, is that he has to rely on the fastball more than you would think for him to be able to get some big outs late."
Neither starter figured into the final decision. Tampa Bay left-hander Drew Smyly gave up four runs, seven hits and three walks in five innings, striking out seven.
Minnesota's Tyler Duffey also gave up four runs and seven hits, walking two and striking out eight in 5 2/3 innings.
"Stuff felt good, I just wasn't locating it well," Duffey said. "Morrison and [Longoria], they're just hot. If you throw it over the plate, they're hitting it hard."
Xavier Cedeno got the win, giving up one run in an inning of relief and closer Alex Colome worked a spotless ninth for his 15th save this season.
Tampa Bay, which had lost seven of eight entering the weekend, lost in Thursday's series opener but responded with wins in the final three.
Minnesota has lost six of seven since sweeping the Seattle Mariners at Safeco Field last weekend.
The Twins got on the board in the first inning when Nunez singled, stole second and scored on an RBI single by Joe Mauer.
Morrison's first home run of the day cleared the right-field wall in the top of the second before the Twins posted a three-spot in the bottom of the third to take a 4-1 lead. Park and Grossman started the inning with homers and Byron Buxton's RBI triple gave the Twins a three-run lead.
Morrison hit a two-run blast in the fourth before Longoria hit solo homers in the sixth and eighth to give the Rays their first lead of the day at 5-4.
"It's fun. Any chance they get up, they're going to do some type of damage," Souza said. "You know that the other team is seeing it. It's great that both of them are hot right now because [Morrison] is protecting [Longoria] and [Longoria is] driving in some runs. The rest of the lineup's picking up the dirty work, as well. It's just fun all the way around."
NOTES: Rays OF Brandon Guyer was placed on the 15-day disabled list with a left hamstring strain. Guyer, who is hitting .271 with six homers and 14 RBIs in 40 games this season, said he hopes to be back as soon as his 15 days are up. ... The Rays recalled INF Nick Franklin from Triple-A Durham to take Guyer's spot on the 25-man roster. Franklin hit .158 in 44 games with Tampa Bay last season and is a career .203 hitter in 174 major league games with the Rays and Seattle Mariners. He was hitting .258 with five homers and 23 RBIs in 51 games with Durham this season. ... Twins OF Darin Mastroianni is swinging a bat and progressing from the strained oblique that put him on the disabled list on May 25. ... The Rays continue their road trip on Monday when they open a three-game series against the Arizona Diamondbacks. Rays RHP Chris Archer (3-7, 4.75 ERA) will oppose Diamondbacks lefty Robbie Ray (2-4, 4.74 ERA). ... Minnesota will continue its homestand Tuesday against the Miami Marlins. LHP Adam Conley (3-3, 3.72 ERA) will go against Twins LHP Pat Dean (1-2, 4.15 ERA).