But there he was on Saturday afternoon, standing in front of his locker at Rogers Centre and speaking publicly about No. 601, tying Trevor Hoffman for the most saves and being the unquestioned greatest closer of all time.
Rivera is a rarity not just because of how good he is, but because of how poised, relaxed, consistent, focused and, ultimately, how comfortable he has been as the ninth-inning rock the Yankees have depended on for the last 16 years.
Situations like these are the only ones that rattle him.
"I am uncomfortable, yes," Rivera said, "because, I mean, I don't have this much attention at all. I'd like you guys to just leave it alone and we'll be good."
But a mark like this can't be left alone.
One Mo' to record
After closing out the Yankees' 7-6 comeback win over the Blue Jays, Rivera joined Trevor Hoffman for the most saves of all time, making it only a matter of time before he has the mark all to himself.
Rivera arrived there via an unhittable cutter and a knack for being unhindered by time; something that continues to be on display. In his age-41 season, he has a 2.02 ERA, has converted 42 of 47 saves and is still considered one of baseball's best closers.
"He's the standard by which all are compared," Blue Jays manager John Farrell said, "and at his age, everyone always says you fight the clock, you fight Father Time, but he certainly is defying it."
Few if any would doubt Rivera is the greatest closer in baseball history. On top of a record-tying 601 saves, he has a 2.22 career ERA, a 1.000 WHIP and an 89-percent conversion rate. And that's just the regular season. On the way to five World Series titles (four as closer) he established a few other postseason records: saves (42), ERA (.71) and appearances (94).
The Yankees have gone 632-41 all-time in games in which Rivera has had a chance for a save.
"He certainly has made it look easy," Hoffman said.
"In sports, I can't think of a better guy to play one position," first baseman Mark Teixeira said. "There's arguments, you know. Baseball there's arguments, basketball -- [Michael] Jordan [or] LeBron [James], whoever, there's arguments. But with this one, there's definitely not an argument."
After the Yankees stormed back from a 6-1 deficit with home runs by Alex Rodriguez and Curtis Granderson, Rivera checked in for the ninth with a one-run lead and drew a nice ovation from the 39,288 fans in attendance.
Then Mo mowed through the ninth in typical Mo fashion: A called third strike on Colby Rasmus, a broken-bat groundout by Brett Lawrie and a lazy flyout by Eric Thames.
Afterward, there were no celebrations -- partly because it wasn't a home game, but mostly because 602, as manager Joe Girardi said, "is the big one."
"I think it just puts the stamp, the final stamp on it -- he's the greatest closer of all time," Girardi added. "I don't think in this room we have any question, and as I said, I don't want to take anything away from Trevor Hoffman, but when you've been around Mo as long as I have, you've seen a lot of special things."
Rivera, who had his wife and two youngest sons in attendance, said he hasn't heard from Hoffman throughout his chase, but has tremendous respect for the former Padres legend. He's humbled by the saves record and proud that he'll eventually be the record-holder for the most important number in his job.
But he probably wishes people would just be quiet about it.
"Don't think that I don't appreciate it," Rivera said. "I do appreciate it. But again, I'm a team player and what happens with me is because my team has permitted it. First of all God, and then my teammates. I'm always thankful to my good Lord first and then my teammates."
Alden Gonzalez is a reporter for MLB.com. Read his columns and his blog, listen to his podcast and follow him on Twitter. Gregor Chisholm and Barry M. Bloom contributed to this report. This story was not subject to the approval of Major League Baseball or its clubs.