Steve Vasturia made a pair of 3-pointers in the second overtime and Eric Atkins added 16 points as Notre Dame survived squandering a six-point lead late in regulation.
Vasturia hit the first 3 to give the Irish a 63-62 lead early then added a second with 62 seconds left that gave Notre Dame a 66-64 lead. Pat Connaughton then added a pair of free throws to help the Irish overcome a career-high 30 points and 14 rebounds by Clemson's K.J. McDaniels.
The Fighting Irish (13-12, 4-8 Atlantic Coast Conference) avoided falling below .500 for the first time this late in the season since finishing 14-16 during the 1998-99 season in John MacLeod's last year as coach.
Clemson (15-8, 6-5) lost back-to-back games for just the second time this season.
Both teams squandered chances to win the game earlier. Rod Hall could have given the Tigers, playing on only a day's rest after losing at Syracuse on Sunday, a one-point lead with 4.6 seconds left, but missed the first of two free throws, sending the game into overtime.
The Irish opened a 60-56 lead in the first overtime on a three-point play by Connaughton, but couldn't hang on. The Tigers scored two baskets in the final 10 seconds and Landry Nnoko then stole the inbounds pass. After being fouled by Connaughton with 8.4 seconds left, Nnoko, a 57 percent free-throw shooter, made both to tie the score at 60.
After another turnover by Atkins, McDaniels missed a long jumper at the first overtime buzzer. McDaniels, who also had five blocked shots, was 13-of-24 from the field, while the rest of the Tigers were 11 of 46. The only other Clemson player in double figures was Hall with 12 points.