Tennessee had to battle from behind in the closing minutes and tied the game on a free throw from Cierra Burdick, who missed her first offering but swished the second one.
Graves powered in a layup with .8 seconds left and when LSU's Adrienne Webb's three-point shot missed - though not by much - the celebration began for the Lady Vols, who were coming off a bitter loss at Missouri last Sunday.
Simmons led Tennessee with 18 points, and Graves netted 17. Burdick had a pair of nines in points and boards, and Kamiko Williams added eight points and six boards off the bench despite a ankle sprain suffered in the last game.
Tennessee next faces Ole Miss at home on Sunday.