Atkins scored five straight points in the fifth overtime period to give Notre Dame a 103-100 lead with 15 seconds remaining, and the Irish were able to clinch the game from the free-throw line the rest of the way.
The Cardinals were down three, 27-24, at the half before opening the second half with a 11-2 run to take a 35-29 lead with 14:27 left in regulation.
Notre Dame's leading scorer Jack Cooley had 11 points and 11 rebounds before fouling out with 6:54 left in the game and the Irish down seven, 47-40.
Louisville extended its lead to 56-48 with 50.0 seconds left in the game before Jerian Grant scored 12 points in the last 47 seconds to tie the game at 60-60 and force overtime.
Grant fouled out with 19 points on a reach in foul on Russ Smith with 1:57 remaining in the first overtime. With the game tied 68-68 with less 12 seconds remaining, Smith missed a long three-point attempt as time expired to send the game to a second overtime period.
Smith had another opportunity to break a 75-75 tie with 15 seconds left in the second overtime but missed a running layup as time expired to force a third overtime period.
Smith had a third opportunity to end the game with 3.7 seconds left in the third overtime and the game tied 83-83, but his floater in the lane hit back rim as the buzzer sounded to send the game to a fourth overtime period.
Notre Dame trailed 93-91 with 19.6 seconds remaining in the fourth overtime period when Garrick Sherman put back a Zac Auguste miss at the rim to tie the game 93-93 and force a fifth overtime period, where Atkins was able to lead Notre Dame to a win.
Atkins finished the game with 14 points on 5-of-19 shooting from the field.
The loss snapped Louisville's three game winning streak and dropped them to 19-5 on the season and 7-4 in the Big East. Notre Dame improved to 19-5 and 7-4 in conference play with the win.