Ragland had 17 points, Washburn 16 and Bohannon 15 for the Miners (3-4), who led by as many as 18 points in the second half. Bohannon also pulled down 10 rebounds and Jacques Streeter had seven assists for UTEP, which shot 52 percent from the field.
Connor Hill led Idaho (3-5) with 16 points.
The Miners pulled away with an 18-3 second-half run that gave them a 52-34 lead with 12:16 remaining. Washburn had nine points in the spurt, Bohannon added six and Ragland buried a 3-pointer to account for all of UTEP's scoring.
Idaho fought back and got within two points on two occasions, at 60-58 and 62-60. But Streeter hit a jumper with 32 seconds left and Washburn sank two free throws with 9 seconds remaining to secure the win.