No. 1 Auburn lost 90-81 to No. 6 Florida earlier in the day, opening the door for Duke to claim the top spot with a win.
Tyrese Proctor had 23 points and Flagg had 18 points on 6-of-17 shooting for Duke (20-3, 12-1).
Clemson trailed by six at halftime, but used a 12-0 run in the second half to take a 56-49 lead with just under 10 minutes to go.
Hunter sealed the win by blocking Proctor's layup with 7.9 seconds left.
Takeaways
Duke: The Blue Devils depth was impacted with Mason Gillis missing his second straight game with an illness. Flagg had just four points in the first 34 minutes of the game.
Clemson: The Tigers showed plenty of grit bouncing back from an 89-86 triple overtime loss to Georgia Tech on Tuesday night. Clemson also beat then-No. 4 Kentucky at home in December.
Key moment
Flagg's slip proved costly with 14 seconds, resulting in a huge turnover with the Blue Devils trailing by two.
Key stat
Clemson won despite making just 13 of 22 free throws.
Up next
Duke hosts California on Wednesday night. Clemson hosts North Carolina on Monday night.
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