Arthur played well in the first half, but struggled late as Carter (who beat Arthur's squad by nearly 30 last year) rallied.
"He plays like he's 6-11," Carter coach Rob Wright said.
Wright said he kept telling his team while it trailed that its shots would eventually start falling.
"This is a good, strong, fighting team," he said. "They stayed with it and stayed with it."
Arthur dominated in the first half, scoring 19 points, including SOC's first 14. Guard Kendrake Johnigan helped SOC stay in it in the second half, in which he scored 15 of his 17 points.