So if Rivera didn't make himself the Sandman, who did?
According to Michael Bonner, the Yankees' senior director of scoreboard and broadcasting, Trevor Hoffman inadvertently had a hand.
Attending the Padres' run to the World Series in San Diego back in 1998, members of the Yankees' upper brass saw how enthusiastically the crowd reacted when Hoffman entered to AC/DC's "Hells Bells."
"The Yankees executives who were there saw the great entrance and said, 'Wow, we need something like that for Mo,'" Bonner said.
Bonner started with the team in 1999, so among the first orders issued to him and scoreboard director Joe Pullia were to find a suitable song that would accompany Rivera on his charge out of the bullpen.
Before "Enter Sandman," two Guns N' Roses songs -- "Welcome to the Jungle" and "Paradise City" -- were actually used in games early in 1999, to lukewarm reception.
"It just didn't have that feel," Bonner said.
Mike Luzzi, then a freelance crew member with the scoreboard team who was also working at MTV, agreed.
"They were trying a bunch of different songs, and I remember yelling at the guys, 'Nobody's going to catch on to this. It's not working,'" Luzzi said.
"I've got to tell you, after Mo is gone, we won't use ['Enter Sandman'] for anyone else. It's meant for the greatest of all time."
-- Michael Bonner, Yankees senior director of scoreboard and broadcasting
So on a Saturday morning, Luzzi lugged his own CD case to Yankee Stadium from Manhattan, pointing to Metallica's self-titled 1991 album and suggesting everyone listen to the first track on the disc.
"We needed something cooler, more ominous," said Luzzi, now a vice president at Turner Sports. "Our job was to try and get the building rocking. The gist of it worked, beginning to put the other club to sleep."
The opening lyrics seemed appropriate to accompany Rivera's now-legendary cutter: "Say your prayers little one, don't forget my son, to include everyone, I tuck you in, warm within, keep you free from sin, 'til the Sandman he comes."
"So we used it that game, and it just had that feel -- the entrance, the way everything comes on," Bonner said. "That was it; that was his song. It stuck from that point on."
In the years since, Rivera and "Enter Sandman" have become intertwined. Though Metallica isn't his style -- he prefers Christian music -- Rivera met lead singer James Hetfield before a 2005 game and sometimes inks autographs using the song's name as an inscription.
When the Mets signed Billy Wagner as their closer in 2006, there was actually a stir that Wagner would dare to use Rivera's entrance song in the same city (in fairness, Wagner also began using "Enter Sandman" in 1999 with the Astros), but Rivera didn't mind.
"It's not part of my identity," Rivera said. "People identify it [with me], but that's it. I wouldn't say that's my identity. To tell you the truth, I have to do one thing. I go out there and pitch."
When Rivera says that the song is not a big deal to him, Bonner believes it.
"For years, he couldn't tell you the name of the song, he couldn't tell you that it was Metallica," Bonner said. "I used to tease him when he'd ask me for something, and I'd say, 'All right, that's it, I'm not going to use "Enter Sandman" anymore.' And he was like, 'I don't care.' I think the fans care about it more."
The fans do love it, and the band has also embraced the connection.
When Metallica played the Rock and Roll Hall of Fame concert at Madison Square Garden in October 2009, their representatives called the Yankees for footage of Rivera's entrance that could accompany the song.
But once Rivera is no longer closing games for the Yankees, Bonner said, the song will be retired at Yankee Stadium along with him.
"I've got to tell you, after Mo is gone, we won't use that for anyone else," Bonner said. "It's meant for the greatest of all time."