Rivera worked a perfect ninth inning for his 42nd save of the season, and tied Trevor Hoffman's mark for the most all-time with 601.
Entering in the ninth to protect the one-run edge, Rivera caught Colby Rasmus looking at a third strike, then got Brett Lawrie on a grounder to first before Eric Thames lined out to center for the third out.
"It's pretty much what Mo's done his whole career," said Yankees manager Joe Girardi. "What can you say about Mo. We've seen a lot of special things."
Rivera could get a chance to break the record on Sunday in Toronto. The Yankees then open an eight-game homestand on Monday with a makeup game against Minnesota.