Eubank finished with 15-of-24 passing for 232 yards for the Bulldogs (6-3, 4-2 Southern Conference). Williams ran for 156 yards on 27 carries.
The Catamounts' Troy Mitchell ran it in from the 3 for the first Western Carolina score with 2:25 left in the first half.
A pair of Reece Everett field goals in the second half put it out of reach for Western Carolina.
Mitchell tightened the gap in the final minutes, taking the Catamounts (6-4, 4-2) 85 yards in 11 plays and scoring his second rushing touchdown. He also threw for 262 yards and another score.