Last week, Costner's band recorded the song "It's All Up to You," as a salute to the 2008 American League East Division champion Rays.
While Costner acknowledged that young squads such the Rays favor the hip-hop genre, he hopes they appreciate his band's rock 'n' roll tune regardless.
"I felt in the back of my head this could work for them," he said. "Lyrically, we added some lines that metaphorically are where they are at."
The song, which is about overcoming adversity, has snippets of the Rays radio highlights and includes the chorus:
You got to swing for the fence, give a hundred percent,
Dust yourself off, get up and do it again.
You're the only one that can make your dreams come true.
You're the only one, it's all up to you.
Maddon and Costner met initially when the Rays skipper was with the Angels organization, and they have stayed in close contact.
Costner has starred in a few baseball films: "For Love of the Game," "Field of Dreams" and "Bull Durham," and is also a producer and Academy Award-winning director.
"There's something about baseball," he said. "It's a slower game than others, but it is part of our fabric. When a team wins, when a town starts to win and it never has, it's something really, really special."
Costner calls the song a "gift" to the Rays, and was happy to get Maddon's stamp of approval.
"Joe's word back to me on his computer was it was 'tasty,'" Costner said of the skipper's initial reaction. The Rays first heard the song early Saturday morning, upon clinching the division title.
"It was Joe's song, and he played it all the way -- stadium level," Costner said.
The tune was also played during Monday's postseason rally in St. Petersburg's Straub Park. Modern West performed at the park last November, during the Rays Uniform Launch, an event Costner dubs one of the "great nights" he experienced with his band.
Costner is "definitely" pulling for the Rays in the postseason.
"Short of the Dodgers being in there, it's going to be the Rays," said the California native. But even if the two teams do square off in the World Series, don't count on Costner to turn his back on Tampa Bay.
"I won't be rooting against them," he said.
Brittany Ghiroli is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.