Woodard broke a tie game with 3:29 left with a 3-pointer, then his jumper with 1:49 sealed the win. Adonys Henriquez's three-point play drew UCF to within two with 1:23 left, but Daiquan Walker's jumper with one second left missed and Tulsa hung on.
Tulsa (8-5, 1-0 American Conference) scored the first eight points of the game, and another 8-0 run later in the half helped them build a 36-21 lead at intermission.
UCF (7-5, 0-1) erased the entire deficit over an 8 minute span in the second half, including back-to-back 3-pointers by Henriquez to cap a 21-7 run, tying it at 49 with 6:06 remaining.
Woodard ended with 14 points on 6-of-17 shooting, including just 2 of 10 from beyond the arc.
Henriquez paced UCF with 17 points, including four 3-pointers.