Rashad Smith added 17 points for Tulsa (10-11, 5-2 Conference USA) as the Golden Hurricane shot 57 percent from the field.
Tulsa jumped to a 47-31 halftime advantage, led by 13 first-half points from Woodard. Lee Evans hit back-to-back 3's midway through the first half before Woodard scored on two consecutive possessions to give Tulsa a 27-16 lead. The Golden Hurricane kept a double-digit lead for good after Smith's basket with 6:52 left in the first half.
Tulsa has won six of its last eight games. The game marked the 51st meeting between the schools, but first since 2006 when North Texas earned a 65-63 win.