"Our gameplan was to keep him out of the game, because if he came in, we weren't going to win," Giambi said. "Game over."
Rivera has had that impact on many teams during his Hall of Fame career, frustrating opposing hitters with his trademark cutter en route to 400 saves.
"Pretty much, you think the game is over when he comes in," Johnny Damon said. "You know you have to turn it up a notch if you want to have a chance. That, or you have to hope his cutter cuts so much that he walks us or hits us."
"I was once asked what my favorite thing was about pitching in New York," Mike Mussina said. "Mariano was my answer. To know that he's out there in the bullpen, it's comforting to know you have somebody who is going to handle those last three outs."
Whether someone has played with Rivera for a decade or a half-season, the overwhelming admiration that his teammates have for him is unanimous.
"He's better than any guy I have ever seen," said Derek Jeter, who came up through the Minors with Rivera. "The most amazing thing is Mo's demeanor; not too many people have what he has. He's never intimidated, he'll challenge anyone, and you can't tell from his expression whether he was successful the night before or if he failed the night before. You have to have that in the role he has and, more importantly, where he's playing."
"You're always more impressed when you see a guy all the time," Mussina said. "You get to see him come in three days in a row, or pitch three innings to win a game, comes in with the bases loaded and one out. Being on his team, you see it all."
Jeter has never had the pleasure of stepping into the batter's box during a regular-season game, but he faced Rivera once a few years back during an intrasquad game in Spring Training.
"I blooped a hit over second base," Jeter said proudly. "I'm happy that I'll never have to face him. This is where he's going to finish his career."
Damon has faced Rivera 31 times during his career, batting just .179 against him.
"I don't have to face him ever again," Damon said. "That was a real enticing reason to come here."
Rivera's credentials on the mound are without equal when it comes to the modern-day closer, but it is Rivera's personality away from the mound that has made the biggest impact on his teammates.
"He comes in here and picks everybody up," Jorge Posada said. "He's always got a smile on his face, and people out there don't see that. In the clubhouse, he's completely different than the guy people see on the mound. He's a great friend and a great person."
"When you compete against someone, you only see that side," Giambi said. "When you get to know him in here, you see what a kind person he is. You wouldn't necessarily think that if you only saw him on the mound. He's so menacing out there."
"Mo reaches out to everybody; he's a great teammate and motivator, especially to young guys," Bernie Williams said. "He likes to take them under his wing, share his faith with them and take care of them. As good a guy as he is, he still has the killer instinct to go out there and do what he does."
Rivera will be remembered as one of the greatest -- if not the greatest -- closers in baseball history. But even a player of his stature encounters tough times on the field, and Rivera is no different.
The difference between Rivera and others in his position is how he dealt with those bad days. Instead of letting them cloud his mind, he learned from those experiences and used them to make himself better.
"When he gave up the home run against Cleveland in '97, everyone wanted to see how he would respond; you saw how he responded," Jeter said. "Same thing with Arizona in 2001. Mo is human. In his position, he's going to fail from time to time. You never expect it, but you know it's going to happen from time to time. People always ask, 'What's wrong with Mo?' Nothing is wrong with Mo."
"He's able to forget things real quick. There's nobody like him," Posada said. "When it's all said and done, he'll be the best closer ever -- if he's not already. If we don't have Mariano Rivera, we don't win four World Series. It's as simple as that."
Rivera is now the fourth pitcher to reach the 400-save mark, but he's far from done. That's good news for the Yankees, who will eventually have the near-impossible task of replacing him when he decides to hang up his No. 42 jersey for good.
"He's a difference-maker; you rely on him so much, you can't even put it in words," Giambi said. "He's in a class by himself. I can't think of anyone who is even close."
Mark Feinsand is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.