The Cougars blew open a close game midway through the first half with a 26-7 run.
BYU shot 51.7 percent from the field, and out-rebounded the Roadrunners 46-18. Davies had 10 rebounds to go along with his 22 points.
The Cougars built a 20-point halftime lead at 48-28 and never looked back.
It was the fifth straight game with at least 20 points for Haws, tying him with Danny Ainge, Kresimir Cosic and Michael Smith for the second-longest streak to start a season in school history. Devin Durrant scored 20 or more in seven consecutive games to start the 1983-84 season.
Josh Sharp had 8 points and 6 rebounds, while Craig Cusick contributed 7 points and 5 assists.
BYU (3-2) next hosts Cal-State Northridge at 7:00 p.m. Saturday night at the Marriott Center.