Detroit did not make any changes to its 25-man roster for the best-of-seven series. Teams had until 10 a.m. Saturday to submit their rosters.
Adding Eppley gives the Yankees 12 pitchers for the series. The 27-year-old right-hander was 1-2 with a 3.33 ERA in 46 innings over 59 relief appearances.
Nunez was 1 for 5 in the five-game division series win over Baltimore, starting Game 2 as the designated hitter and coming into two other games off the bench.
Detroit is carrying 11 pitchers.