Kendall, a 42-year-old lifetime grinder, picked up his first Nationwide Tour win since he won his only other two titles in 1994, hanging on with a 1-under 70 in the final round.
Claxton, looking for his first win in six years, eagled No. 1 on Sunday and later birdied his last two holes to finish off a 6-under 65
The duo finished tied at 16-under-par 268.
Jarrod Lyle shot a 68 and ended alone in third place at 15-under 269. D.J. Brigman (66) and Tom Byrum (70) shared fourth place at 13-under 271, while Chris Tidland (67) and Tag Ridings (71) were a shot further back at 272.