Isaac Paredes added a solo homer in the eighth inning, his 29th of the season, for the Rays, who hold a 6 1/2-game lead over Seattle in the race for the top AL wild card.
“This could be a team that we would play some more in the playoffs,” Paredes said through a translator. “So, the adrenaline hits when you play a team like this. They're a good team.”
Tampa Bay started the day four games behind AL East-leading Baltimore. The Mariners entered play trailing first-place Houston by a half-game in the AL West.
Chris Devenski (4-4) got two outs in the seventh and earned the win, while Pete Fairbanks worked the ninth and earned his 21st save in 23 chances.
Julio Rodríguez, Cal Raleigh and Eugenio Suárez homered for the Mariners.
“I was hoping we had enough offense,” Seattle manager Scott Servais said. “You've got to give them credit, they came back.”
Pinto went deep on George Kirby's 102nd and final pitch before Ramírez gave the Rays a 6-4 advantage on his drive off Isaiah Campbell (4-1).
“The home run by Pinto kind of gave us energy and gave us a lot more motivation to keep on going,” Paredes said.
Pinto has homered in three of his last four games after entering the stretch with three career long balls,
It was Ramírez's first homer since June 8 and ended a career-worst 55-game homerless drought.
Kirby gave up four runs and five hits over 6 1/3 innings.
Rodríguez gave Seattle a 3-2 lead on his 28th homer, a solo shot in the third inning off Taj Bradley. He is hitting .336 with 15 homers and 52 RBIs since July 1.
The 22-year-old Bradley worked a career-high 6 1/3 innings. The rookie right-hander allowed four runs and six hits.
Raleigh made it 4-2 with his 27th home run in the fifth inning. Suárez went deep in a two-run second as Seattle tied it at 2.
An usually wild Kirby loaded the bases on two walks and a hit batter in the first before Paredes had a run-scoring single that left fielder Dominic Canzone appeared to lose, and Josh Lowe followed with a sacrifice fly that put the Rays up 2-0.
Kirby had walked just 14 batters over his previous 26 starts this season, and had not issued one in a career-high five straight outings.
“Really awesome job by George to rebound,” Servais said.
Commissioner Rob Manfred met with players from both teams before batting practice as part of a stadium tour. Rays player rep Tyler Glasnow said Manfred did not talk about Tampa Bay All-Star SS Wander Franco, who is on administrative leave indefinitely by MLB while authorities in the Dominican Republic investigate him for an alleged relationship with a minor.
Seattle RF Teoscar Hernández extended his career-best hitting streak 17 games with a double in the third inning.
In partnership with the Children’s Dream Fund, 19-year-old Austin Majors of Holiday, Florida, symbolically signed a contract with Tampa Bay president of baseball operations Erik Neander. His dream was to meet Rays manager Kevin Cash and the pair delivered the lineup card to the umpires. Majors had a heart transplant at three months old, and has cystic fibrosis, autism, scoliosis, epilepsy and is blind in one eye.
Rays RHP Aaron Civale (7-3) will face Seattle on Saturday. Civale, acquired from Cleveland on July 31, has gone 2-1 but lasted 5 ⅓ innings or fewer in five of six starts. The Mariners didn't announce their starter.
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