Washington stole the ball from Nick Russell and scored to put the Cowboys (13-0) ahead by three. Russell committed another turnover in the closing seconds as the Mustangs (10-5) fell to 5-1 at home.
Larry Nance Jr. added 12 points for Wyoming and Josh Adams had 11. Russell led SMU with 17 points and Cannen Cunningham had 14 points and 11 rebounds.
Neither team managed more than a five-point lead.
Wyoming next opens Mountain West play by hosting Boise State on Jan. 9, while SMU starts Conference USA action against Tulsa on Sunday. That game pits SMU coach Larry Brown against Tulsa’s Danny Manning, the Final Four Most Outstanding Player from Brown’s Kansas team that won the 1988 national title.