Montorie Bridges, ranked No. 8 at 133 pounds, gave the Cowboys a 19-7 lead with a 4-0 decision, but the Bulldogs got one victory by pinfall and three by decision to get the dual win.
Tate Samuelson earned a major decision at 184 and Stephen Buchanan (197) and Jake Svihel (125) won by forfeit for the only other Wyoming victories.
The Cowboys return to the mat Sunday when they host No. 7 Oklahoma State.
