Woodard was 10 of 18 from the field including three 3-pointers for Tulsa (4-1), which never trailed the Tigers at any point in the game.
Scottie Haralson scored 16 points for the Hurricane and Shaquille Harrison added 12.
Tulsa led 35-30 at the break but sprinted out of the locker room to go on a 9-0 run before the Tigers were able to score their first basket at the 16:39 mark. Jackson State (0-2) cut the Hurricane’s double-digit lead with 10:49 remaining at 53-51 but Tulsa finished strong, outscoring the Tigers 33-15 the rest of the way.
Kelsey Howard scored 25 points and had nine rebounds while teammate Christian Williams had 23 points. Each hit five 3-pointers in the loss for Jackson State.