ST. PETERSBURG, Fla. -- Jacob Realmuto had a remarkable start to his big league career.
"You can't really ask for much better from my standpoint," Realmuto said.
Realmuto drove in two runs on his first big league hit, a fourth-inning single, and added a sixth-inning RBI single.
Marlins infielder Justin Bour also made his major league debut as the designated hitter and had an infield single during the fourth for his first hit. He picked up his first RBI with a single in the seventh.
"It's fun to have young kids in there, watching them get their first at-bats in the big leagues, and watching them have a nice day and for us to get a win," Miami manager Mike Redmond said.
Ozuna's two-run homer put Miami up 11-6 in the ninth. Giancarlo Stanton hit his 17th home run, a two-run shot during a three-run seventh that made it 9-5.
The Marlins beat the Rays for the fourth straight time in a home-and-home interleague series. Miami has 12 straight interleague wins, including seven this season.
"It's not easy sweeping a team," Redmond said. "Fortunately our offense just kept the pressure on."
Kevin Kiermaier and Ben Zobrist homered for the Rays, who matched the longest skid in the majors this season. Boston dropped 10 straight from May 15-25, with Tampa Bay handing them the last three losses in the streak. The Rays haven't won since.
"This team's too good for that," Rays manager Joe Maddon said. "There's too much talent on this team to go through this particular moment. I'm really not into the blame game. We're all culpable when it doesn't go well. I mean that sincerely. It's a good ballclub. These are good baseball players."
Tampa Bay has the majors worst record at 23-38 and are 14 games behind AL East-leading Toronto.
Redmond was ejected by first base umpire Bill Miller for arguing after Desmond Jennings RBI double down the first- base line got the Rays to 9-6 in the seventh.
"I clearly thought that ball was foul," Redmond said. "When I got out there, I reaffirmed the fact that it was foul, but I couldn't convince him."
Jacob Turner (2-3) allowed five runs and eight hits over 5 1/3 innings for Miami. He had been 0-11 in his previous 19 road starts.
Matt Joyce had an RBI triple and pinch-hitter Jerry Sands hit a run-scoring single that cut the Rays' deficit to 6-5 later in the sixth. Sands' hit ended a stretch that saw Tampa Bay go 0 for 34 with runners in scoring position.
Ozuna hit an RBI single and Realmuto had his two-run single to help the Marlins take a 3-1 lead in the fourth.
Odorizzi gave up four runs and seven hits in five-plus innings.
Tampa Bay pulled even at 3 on fifth-inning solo homers by Kiermaier and Zobrist. James Loney put the Rays ahead 1-0 on a sacrifice fly in the first.
The Rays held a moment of silence for team senior adviser Don Zimmer, who died Wednesday night at the age of 83. ... Tampa Bay C Ryan Hanigan (right hamstring tightness) ran the bases and could start a minor league rehab assignment Saturday. ... Marlins SS Rafael Furcal (left hamstring strain) moved his rehab assignment from Single-A Jupiter to Double-A Jacksonville.