Atkins' basket with 1:44 to play in the fifth extra period put Notre Dame (19-5, 7-4 Big East) ahead 102-100 and the junior guard added a free throw with 19 seconds remaining to help seal the longest game in Big East Conference history.
Atkins finished with 14 points and five rebounds. Jerian Grant added 19 points and six helpers before fouling out as the Irish bounced back from a Monday loss to Syracuse.
Garrick Sherman (17 points), Pat Connaughton (16, 14 boards, seven assists) and Cameron Biedscheid (14 points) also played key roles for Notre Dame in just the fifth Division I game to reach five overtimes since 1996-97.
Chane Behanan provided 30 points and 14 rebounds for the Cardinals (19-5, 7-4), whose three game-winning streak was snapped.
Luke Hancock put in 22 points and Russ Smith supplied 21 and 10 rebounds in Louisville's epic loss.