NEW YORK — It's official: Mariano Rivera stands alone.

The Yankees reliever, already considered by most to be the greatest closer of all-time, passed Trevor Hoffman today for the career lead in saves with 602. By closing the door on the Minnesota Twins in the Yankees' 6-4 victory at Yankee Stadium, Rivera also slammed shut any debate about his standing among the game's greatest relief pitchers.

Rivera is now into uncharted territory. He hasn't simply passed Hoffman, he's blown by him. By the time Hoffman recorded the last of his 601 saves he was in the midst of decline. At age 41, Rivera remains a dominant force. His 43 saves rank second in the American League to only the Detroit Tigers' Jose Valverde.

It came after the Yankees handed A.J. Burnett a 5-0 lead behind Curtis Granderson''s two-run homer. But they watched Burnett nearly give it all away. He didn't survive the fifth, but after the Twins cut the deficit to 5-4, the bullpen held the line the rest of the way.

Alex Rodriguez knocked in an insurance run in the sixth inning. And in the bottom of the eighth, the fans let out a large roar when Nick Swisher bounced into a double play, preserving Rivera's chance to make history.

Chants of “Let's Go Mo!” filled the Stadium as Rivera worked to reach the milestone that he has called “the big one,” the all-time saves mark.

After Rivera's final pitch — a cutter that crossed the plate at 93 miles per hour to freeze Chris Parmelee — he was mobbed by Yankees teammates who hugged and congratulated him. As Rivera walked off the mound, catcher Jorge Posada, behind the plate for so many of Rivera's saves, pushed the closer back onto the mound so the Yankee Stadium fans could show their appreciation for the all-time saves leader.

Rivera admitted that he's been uncomfortable with the attention that has come with his pursuit, which has been marked by talk of his place in history.

“It doesn't make me better or worse,” Rivera said. “People are going to say whatever they're going to say. I feel normal. I feel just that I have to do my job.”

For 16 years, nobody has done that job better than Rivera, whose 41 postseason saves are the most of all time. His work in October, combined with his regular season dominance, have made Rivera's case for greatest ever an easy one.

“There's no doubt,” teammate Mark Teixeira said. “This list, he deserves to be on top of it. In sports, I can't think of a better guy to play one position. There's arguments. Baseball, there's arguments. Basketball. Jordan, LeBron, whoever. There's arguments. With this one, there's definitely not an argument.”

Perhaps the only question that remains is how far Rivera can push the record. He signed a two-year contract extension before this season and has shown little sign of slowing down.

“He will pitch until 50,” said former Yankees catcher Jose Molina. “Because he can.”

More coverage:

• Complete coverage of Mariano Rivera's record on NJ.com

Teixeira said he doesn't see an end in sight, either.

“Mo's not done,” he said. “He's not going to be done until someone pulls that uniform off him.”

As for his own future, Rivera points out only that he's under contract for next season, but makes no pronouncements after that. But no matter his future, with the save No. 602 in his pocket, Rivera is assured that he will go out on top.

“I won't say proud. I would say thankful,” Rivera said last week. “I'm thankful to the Lord. I'm thankful to my wife, my kids, my family, the organization, my teammates. That's what I'm thankful for, for where God has put me and for what God has done for my life, and that involves everything. More than proud, I'm thankful.”

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Marc Carig: mcarig@starledger.com