Erwin Dudley led the Tide with 16 points and eight rebounds on eight-of-11 shooting. Kenny Walker blocked four shots, pulled down six boards, and had nine points in 22 minutes of action.
Alabama head coach Mark Gottfried was pleased with his big men's performance.
"We wanted to go at them early and establish an inside presence," he said. "I thought we did that with Kenny and Erwin."
Rod Grizzard added 13 points shooting 50 percent from the field.
Bama shot a collective 44 percent from three-point range and was 34-of-66 from the field.
Jason Coleman led the Cowboys with 16 points on six-of-17 from the floor. Adrian Johnson had a double-double with 11 points and ten rebounds.
Alabama's next game will be at home Monday night at 8 p.m. when the Tide will host the UT-Chattanooga Mocs on Fox Sports Net.