New Orleans (4-7, 1-2 Southland Conference) held on late after Harrison Hawkins hit a 3-pointer with 38 seconds left to cut the Privateers' lead to 83-81. With New Orleans up 85-81, McPhearson grabbed an offensive rebound after a missed free throw, and then made two free throws himself to help preserve the win.
Christavious Gill scored 17 points for the Privateers and Kevin Hill added 14. Cory Dixon added 12 points and 14 rebounds, helping New Orleans to a 42-33 rebounding advantage.
Hawkins had 19 points and five assists for Abilene Christian (6-9, 0-1). Parker Wentz scored 16 and LaDarrien Williams contributed 15 points, nine rebounds and five assists.
Abilene Christian was playing its first Southland Conference game since the 1972-73 season, while New Orleans hosted its first conference game in more than four years.