Hoffman saved 601 games during an 18-season career that ended when he retired this past offseason. The right-hander spent the majority of his career with the Padres and became a face of the franchise through his longevity and success.
Rivera has been a face of the Yankee franchise since breaking into the majors with them in 1995.
Since then, he's worked scoreless ninth inning upon scoreless ninth inning, during the regular season and the playoffs. His performance Tuesday put another stamp on a New York victory, the Yankees' third straight.
"It feels great, it's a great number," Rivera said. "I think the next one's the biggest. I thank God for that moment."
He was in position to make the save after A.J. Burnett (10-11) struck out a season-high 11 and allowed two runs in six innings. He picked up his first victory since August 15 and won for just the second time in his last 13 starts.
Robinson Cano homered and plated the decisive run in the sixth inning for New York, which claimed a 9-3 victory in the opener of this three-game series on Monday. The Yankees maintained their four-game lead in the AL East over Boston, which beat Toronto on Tuesday.
Charlie Furbush (3-9) allowed three runs in 5 1/3 innings to take the loss, Seattle's fourth in a row.
Cano put the Yankees on the board in the second inning, when he led off by blasting his 26th homer of the season.
Jesus Montero and Andruw Jones followed with a single and double, respectively, to get a rally started. But Furbush limited the damage with strikeouts.
He fanned Russell Martin, who had missed the last two games with a bruised thumb, before allowing a run to score with a wild pitch. Furbush then struck out Eduardo Nunez and Brett Gardner to end the inning.
Burnett hit a batter in the third inning to load the bases, leading to Olivo's game-tying sacrifice fly.
"We let him off the hook early," Mariners manager Eric Wedge said of Burnett. "He was struggling early on in the ballgame and we had opportunities, and that's when we needed to take advantage of it."
But the Yankees regained the lead in the sixth, which Nick Swisher began with a double. Mark Teixeira's base hit put runners on the corners for Cano, whose fielder's choice plated a run.
After Burnett worked a clean bottom of the sixth, Rafael Soriano pitched a 1-2-3 seventh and David Robertson survived the eighth. The Mariners had the bases loaded with two away, but Robertson struck out pinch-hitter Trayvon Robinson.
Then, Rivera took over. He fanned pinch-hitter Wily Mo Pena to start the inning before Ichiro Suzuki reached on a single. But after Rivera struck out Kyle Seager, Suzuki was caught stealing second to end the game.
Rivera recorded his 41st save of the season...Swisher was back in the outfield, starting in right, after playing at first base for Monday's game. He had missed three consecutive contests with an elbow issue before returning Monday...Derek Jeter singled leading off the game to extend his hit streak to 12 games...Furbush has dropped five consecutive starts.