Secean Johnson added 10 points for UC Riverside (6-5).
Menno Dijkstra's jumper made the score 51-38 for the Highlanders with 8:39 to play, the largest lead of the second half.
With 2:13 to play, however, Jaylen Franklin's jumper brought Abilene Christian to within 59-53. A Duran Porter free throw and Jovan Crnic's layup with 33 seconds left cut UC Riverside's lead to 59-56.
The Highlanders raced to a 21-7 lead in the game's first 10 minutes and went to the break with a 31-20 lead.
Crnic finished with 18 points and Austin Cooke had nine rebounds for Abilene Christian (4-6).