The story coming into Tuesday’s game at Tropicana Field was MLB’s top prospect Wander Franco making his debut for the Rays. 

It was a story that gained even more momentum when Franco smashed a game-tying, three-run homer against Eduardo Rodriguez in the bottom of the fifth inning. 

But the Red Sox have their own story they want to keep building on, as perhaps the biggest surprise team in MLB so far this season. 

And that gained some more steam Tuesday night, with the Sox outlasting Franco and the Rays with a grind-it-out, 9-5 victory in 11 innings.

• Box score

Though it wasn’t the prettiest game manager Alex Cora’s team has played this season, Boston (44-29) stayed the course and extended its lead in the American League East to 1 1/2 games over the Rays. Tampa Bay, scorching-hot last month with an 11-game winning streak, has lost seven in a row.

“If you take a look at the guys we have on this roster, they have to earn everything that they have,” said Cora. “We have a bunch of grinders, a bunch of guys that on other teams, they didn’t play that much, but they’re getting their opportunities to play here. We just like to play baseball.

“It’s a good baseball team and we still have to get better in certain things. I keep saying it. But at the end of the day, you tell us where or when or what time. It doesn’t matter if it takes two hours and 45 minutes or whatever it took today. We push to the end no matter the result. It’s a testament to who they are. I’m very proud of them.”

The Sox are now 4-0 against the defending AL champions this season. Boston found a way to prevail despite errors by Xander Bogaerts and Rafael Devers in the bottom of the first, and outs on the bases by Devers, Bobby Dalbec and Alex Verdugo in the late innings.

“At the end of the day, it’s a big league win against a team that … they’re the American League favorites,” said Cora. “Everybody said coming into the season that they have a chance to get back to the World Series and we did a good job against them.”

For all the grinders that Cora mentioned, the Red Sox also have some studs in their batting order, including Devers.

The star third baseman atoned for his costly error in the first and his baserunning miscue in the eighth when he smashed a two-run double (exit velocity of 104.1 mph) into the right-field corner in the 11th inning that eluded Rays first baseman Yandy Díaz. Devers leads MLB with 23 game-tying or go-ahead hits this season.

Though Devers is still trying to be more consistent in the field, his improved maturity with the mental side of the game is what allowed him to come through when it mattered the most.

“Obviously I made that error that could have really cost us, but I just put it behind me,” Devers said. “I just turned the page and focused on ways I could help the team win. That’s something I was able to do today so thankfully I was able to execute. That’s part of baseball. I’m going to make errors and I’m going to have to remember that. Don’t let it just sit on me. I just have to continue to play the game that I know how to play.”

Meanwhile, the Red Sox just keep finding a way.

This, even though their projected ace going into the season -- Rodriguez -- hasn’t been in sync for the past month.

If not for the shaky defense Rodriguez had behind him in the first inning, perhaps he would have recorded his first win since May 7. But he did pitch six innings for the first time since May 12 and recorded his first quality start since April 25.

“After everything I’ve been through the last six, seven, eight starts, this start was really good for me,” Rodriguez said. “I went six innings, and I felt good with all my pitches.”

If Franco’s career goes the way people expect it will, Rodriguez could one day be the answer to a trivia question as the first pitcher to be taken deep by the exciting phenom, who is just 20 years old.

“What a good player he is, by the way,” said Cora. “The way he controls the at-bats for how young he is and to have this building behind him. I’ve never seen anything like this -- like that -- in this building. For him to slow down the game, they have a special one.”

The Red Sox think they have a special team.

“We’re battling for first place against them, so it’s a big win tonight,” said Rodriguez. “After everything that happened in the game, and the homer I gave up to the kid, the way we scored those runs, I feel like this was a big game for us.”