The victory was overshadowed by a knee injury suffered by the Cowboys' top player, Larry Nance Jr.
Nance had 17 points, on 7-of-9 shooting, before he was fouled while fighting through the lane with the ball. He came to a jump stop and then fell to the floor. The Cowboys' leader in scoring, rebounds, blocks and steals stayed on the court for several minutes holding his right knee before being helped off, unable to put any weight on the leg.
"I don't think it looks good," Wyoming coach Larry Shyatt said. "We'll take an MRI. They're setting it up (Wednesday) morning."
Shortly after Nance went down, Sobey, who finished 15 of 17 at the free throw line, sank a pair to put the Cowboys up 40-31. But the Bulldogs rallied to tie it on a 9-0 surge. Tyler Johnson made a 15-footer and drained a 3-pointer during the run and Cezar Guerrero knotted it with a short, high-arcing jumper.
Adams's 16-foot fadeaway broke the tie moments later and the Cowboys eventually built the lead to nine on two occasions. Then weathered a late spurt by the Bulldogs. Harris' floater with 8.8 seconds left drew Fresno State within 70-66, but Wyoming's Riley Grabau made two foul shots to clinch it.
Josh Adams, whose jumper gave the Cowboys the lead for good with 11:21 to play, added 10 points for Wyoming (17-9, 8-5 Mountain West).
Johnson scored 24 points, while Marvelle Harris added 18 and Guerrero 13 for Fresno State (13-14, 6-8), which saw its five-game winning streak snapped.
Fresno State took an early 16-10 lead before Wyoming, behind eight straight points from Nance, went ahead 25-22 at the half.
Wyoming was 33 of 44 at the stripe, while Fresno State was 21 of 25. The Bulldogs were whistled for 31 fouls, many coming down the stretch while playing catch-up. The Cowboys had 18 fouls.
The Bulldogs only had two assists, far below their 12.2 average in conference play.
"There were a lot of things that played into that," Harris said. "Not playing together mostly. Instead of making the extra pass, sometimes we settled."
Shyatt said he could tell by the look in his players' eyes during timeouts that they had the will to overcome Nance's loss.
"I told them in the locker room, 'You're one of the smartest ball clubs I've been around because you find ways.' And tonight they had to find a way without their leader," he said.