With the game tied at 40 with just over seven minutes remaining, The Owls scored eight of the game's next nine points, capped off by a Bishop Mency jumper to push their lead to seven. St. Edwards would get within three after two Frankie Mgbolu free throws, but Rice's Max Guercy sealed it with two free throws.
Mency added 12 points off the bench for the Owls (2-6), while Marcus Jackson finished with 10 points.
Rice held the Hilltoppers to 31.7 percent shooting from the field and 4 of 17 from 3-point range.
Frankie Mgbolu scored 14 points and added five steals to lead St. Edwards. Quinton Lilley came off the bench to score eight points and grab 10 rebounds.