Wright scored seven points and Woodard added five as part of a 16-5 run to open the second half and give Tulsa (2-1) a 49-24 lead with 13:59 to play. Abilene Christian made just seven of 21 shots from the floor in the second half, finishing 15 of 55 from the field for 27 percent.
Wright shot 5 of 5 from the floor and grabbed seven rebounds, and Woodard finished 5 of 11 from the field. Shaquille Harrison dished out five assists and Rashad Ray added four for the Golden Hurricane.
Woodard hit a 3-pointer to give Tulsa an early 23-15 lead, and the Golden Hurricane led by double digits the rest of the way.
Austin Cooke scored 12 points to lead the Wildcats.