Woodard was 6 of 11 from the floor, including 4 of 8 from long range. Smith finished on 5-of-8 shooting and grabbed eight rebounds. Rashad Ray dished out six assists and added 10 points for Tulsa, which shot 25 of 44 from the field (56.8 percent) and outrebounded Tulane 37-29.
Tulsa used an 18-3 run, including four straight 3-pointers, to make it 66-41 with 5:08 to play.
Louis Dabney hit three of his five 3-pointers in the final 1:58 to finish with a career-high 32 points to lead Tulane (14-13, 5-10).