ST. PETERSBURG -- The Rays were down by two and down to their last out with nobody on base in the ninth inning Tuesday night. They were down again in the 10th and the 11th. Then they found themselves one out away from a frustrating, exhausting defeat in the 13th inning.

They were down, but somehow never out.

The Rays came back four times to pull off a wild, 7-6 win over the Angels at Tropicana Field, their first walk-off victory of the season. Amed Rosario sent them home happy after three hours, 29 minutes and 13 innings by legging out an infield single against right-hander Carson Fulmer.

“Sometimes,” manager Kevin Cash said, “you’ve just got to find a way.”

They found one, harrowing and convoluted as it might have been, in MLB’s first 13-inning game of the year, which was tied for the Rays’ longest game played under the current extra-inning rules.

Left-hander Garrett Cleavinger gave up one run in the top of the 13th, as Luis Rengifo stole third and scored on a single by Zach Neto -- the Angels’ first hit since the fourth inning. But Richie Palacios kept the Rays alive with a two-out RBI double to right.

“We were at the field for a long time,” Palacios said, smiling, “so we're trying to get some runs in for the boys. I'm glad I was able to do that there.”

The Angels chose to intentionally walk Isaac Paredes, then Fulmer walked Harold Ramírez on four pitches to load the bases. Up came Rosario, who bounced a 69.5 mph grounder to third baseman Anthony Rendon.

Rosario hustled down the line, beat Rendon’s throw and ran across the bag with his right hand held high.

“I knew as soon as I hit it I was going to be safe. I knew it,” Rosario said through interpreter Manny Navarro.

“That's all I can control, so at that point, that's all I was trying to do is just make it to first base.”

Rosario also played a part in Tampa Bay’s first game-saving rally, which started with two outs in the ninth. At that point, the Rays had only one hit on the night, a fourth-inning single by Palacios, and trailed, 3-1.

But the lineup came to life against Angels closer Carlos Estévez, as Ramírez and Rosario delivered back-to-back singles before José Caballero tied the game with a triple to right field.

The Rays' beleaguered bullpen bent but didn’t break after a quality start by Aaron Civale, as seven relievers combined to permit just one hit (in the 13th), one walk and one hit batter. They allowed three automatic runners to score, but Tampa Bay's lineup answered every time.

“It’s draining when you lose,” reliever Jason Adam said, smiling, “but it's fun when you win.”

Closer Pete Fairbanks gave up a run in the 10th on a sacrifice bunt and a wild pitch. The Rays mirrored that strategy against reliever José Cisnero, as René Pinto dropped a sac bunt -- a rarity for the Rays -- to advance Jose Siri.

Yandy Díaz tapped one back to the mound, and Cisnero -- seemingly distracted by Siri breaking toward the plate on a contact play -- uncorked a wild throw past first base that allowed Siri to easily score the tying run.

Adam immediately found trouble in the 11th, hitting Zach Neto then walking Rendon to load the bases for Mike Trout. Given Trout’s reputation and all the damage he’s done against the Rays throughout his career, Cash joked that he thought about intentionally walking him.

But Adam bore down and got Trout to pop out on a 96.7 mph fastball, his hardest pitch of the day, eliminating the greatest threat in the Angels lineup. They got one run out of it, anyway, as Taylor Ward lofted a sacrifice fly to deep center that Siri ran 93 feet to reel in at the wall.

Adam feared the ball was gone off the bat, but Siri said through Navarro he knew he had it all the way.

“That’s the play of the day. Siri, we've really stressed to him how important his defense is and how he can change a game,” Cash said. “I think you can argue that won the game, gave us a chance.”

Isaac Paredes led off the bottom of the 11th with a single to center to cap a 13-pitch at-bat. That moved Palacios to third base, and Palacios scored the tying run on a double-play grounder by Ramírez. The teams traded zeroes in the 12th, then the Rays finally found a way to end it in the 13th.

“You find out a little bit about your club early on in the season. We're grinding through things right now, for sure. And these guys, they're staying positive,” Cash said. “To win a game like that, you take that as a big moment early on in the season.”