Wynn ran 13 times for 96 yards with his scoring run coming late in the first quarter. Atkins made kicks from 50 and 48 yards in the second quarter, and his 28-yarder stretched the Paladins' lead to 16-3 early in the fourth.
The Mocs got back in it when Isaiah Mack forced Ridge Gibson to fumble the ball at the Furman 14. Nick Tiano tossed a 5-yard touchdown pass to Bingo Morton four plays later to make it 16-10 with 1:49 remaining.
Furman (4-4, 4-2 Southern Conference) recovered the ensuing onside kick to win for the fourth time in five games after starting the season 0-3.
Tiano was 25 of 37 for 154 yards passing for Chattanooga (6-3, 4-3).