Tanner Samson had 10 points for the Phoenix (11-7, 4-2), which was coming off conference wins over Furman and Western Carolina.
Karl Cochran scored 18 points, Lee Skinner had 13 points and a career-high 14 rebounds, and Spencer Collins scored 14 for the Terriers (7-12, 1-5), who have lost three in a row. Wofford had won the past four games against Elon.
Elon shot 23 of 50 from the field to Wofford's 19 of 51, and was 7 of 21 on 3-pointers to the Terriers' 2 of 11.
Wofford led 29-27 at the half, but Davison tied it at 33 on Sebastian Koch's jumper and grabbed the lead for good at 41-39 on Samson's layup with 13:39 remaining.
Forward Kennedy Meeks, who has averaged 9.4 points and 6.5 rebounds at North Carolina, has pulled out of the NBA draft and will return to the Tar Heels.
Cal big man Ivan Rabb could have been selected in the top 10 of the NBA draft. Instead, he's returning to Berkeley to make himself, and the Golden Bears, stronger.
Devin Williams' decision last month to sign with an agent and enter the NBA draft has left West Virginia in a tough spot.