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.
Seton Hall sophomore Isaiah Whitehead will stay in the NBA draft and not return for his junior season.
Washington State's trio of Josh Hawkinson, Conor Clifford and Ike Iroegbu have withdrawn from the NBA draft and will play their senior season with the Cougars.
Gonzaga center Przemek Karnowski, who missed most of last season with a back injury, says he is returning for another year.