Lewis made 17-of-18 free throws and led the Cougars (11-3, 2-0 Conference USA) with 29 points. Coleman scored 24 points, grabbed 12 rebounds and had six assists. He was 8-of-10 from the free throw line.
Qa'rraan Calhoun scored 15 points for Houston while Desmond Wade and Marcus Cousin scored 12 and 10 points, respectively.
Stefon Jackson led the Miners (10-6, 1-1) with 27 points and Kareem Cooper added 21. Randy Culpepper came off the bench and scored 16.
The Cougars outscored the Miners at the free throw line 34-23.