Allman led North Myrtle Beach from the outside, scoring a game-high 24 points and making nine steals that the Lady Chiefs (2-0) converted into easy transition baskets.
Livingston tallied 12 points and pulled down a game-high 14 rebounds, some on the offensive end which she converted into put-back baskets.
Together Allman and Livingston tied the Lady Lions (1-1) in total points at 36, and the rest of the Lady Chiefs proved to be the difference. Marcie Chestnut came off the bench to score six points and grab six rebounds, and backup Lekhandra Cox pulled down seven boards and tallied three points.
North Myrtle Beach jumped out to a 19-9 lead in the first quarter and was never threatened. The Lady Chiefs outscored the Lady Lions (1-1) 18-6 in the third period to put the game away.
The Lady Chiefs play their third straight road game to open the season on Tuesday at Carolina Forest.