With the win, UH improves to 14-0 and extends their home winning streak to 27 straight games, which is the longest home winning streak in the nation.
Davis Jr. hit on six of 11 three-point attempts on his way to 21 points, and added five rebounds and four assists in his 36 minutes on the floor.
The Cougars got help off the bench with 33 points from their reserves. Freshman, Nate Hinton, led the bench brigade with 13 points and eight rebounds, while Fabian White Jr. and DeJon Jarreau each added eight points apiece.
UH welcomes Memphis at 5 p.m. Sunday inside the Fertitta Center as they look to start the season 15-0, and hope to extend their home winning streak to 28 games.