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.
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