Woodson also had four of Memphis' 17 steals as the Colonels turned it over 27 times.
Ricky Tarrant Jr., Trahson Burrell, Dedric Lawson and Nick Marshall all scored in double figures for Memphis (10-4). Burrell led the Tigers with six assists, Lawson grabbed a team-high eight rebounds and Marshall made his first start of the season.
Memphis trailed 14-7 before going on a 43-4 spurt to lead by 39 points at halftime. The Tigers shot 56 percent from the field, including 63 percent from 3-point range, before intermission.
The Tigers finished 31-of-70 shooting (44 percent) with seven 3-pointers.
Johnathan Bell scored nine points to lead Nicholls State (4-11), which has lost eight of its last nine games.