The Tribe, who trailed by as many as 18 points in the first half, rallied to take a 41-40 lead - their first since 8-7 - with 13:27 to go.
Shakir Brown hit a 3-pointer with 1:10 remaining to pull James Madison to 60-58, but Sean Sheldon answered with a basket and Dixon and Greg Malinowski combined to make 6 of 6 free throws down the stretch.
Terry Tarpey added 11 points for William & Mary (15-6, 7-3 Colonial Athletic Association).
James Madison built a 38-26 lead at halftime after making 7 of 18 3-pointers. But the Dukes were just 2 of 16 beyond the arc in the second half