Brummit was 6 of 9 from the field and scored 13 of his 18 points in the second half.
Western Carolina (2-2) led 46-38 with 13:34 remaining and used a 17-4 run in the next 3:31 to win its second straight at home to start the season. Twelve different players scored for the Catamounts.
Jordan Sexton had 13 points and Kevis Jackson 12 for Hiwassee (4-6). Both players went 5 of 8 from the field.
The Catamounts dominated on the glass, grabbing 61 rebounds compared to the Tigers' 36 and leading 29-10 in second-chance points. Western Carolina led by as many as 31 in the second half.