Cochran made 10 of 11 free throws for the Wildcats (5-4, 2-0 Southern Conference).
After losing most of a 21-point lead at the end of the first half, Davidson kept Wofford at arm's length early in the second before pushing it to 47-33 with 11:54 remaining.
Wofford closed to 51-47 on Spencer Collin's dunk with 5:31 to go.
Davidson's Jake Cohen made a layup for a 57-50 advantage with 3:29 left, and the Wildcats held on for the victory.
The Wildcats led 31-10 with 3:36 to go in the first half, but Wagener hit two 3-pointers during a 12-point spurt to pull Wofford to 31-22 at the break.
Florida State's student government has passed a resolution discouraging Seminoles fans from wearing Native American headdresses at games.
The second annual Gavitt Tipoff Games, eight games between members of the Big East and Big Ten to be played Nov. 14-18, will feature Villanova at Purdue in the opener.
Michael Lewis is leaving his assistant coaching job at Butler to take the same position at Nebraska under Tim Miles.