CSU (3-4, 1-1 Mountain West) ended a four-game losing streak to Wyoming (4-3, 2-1) and prevented the Cowboys from going 3-0 in conference play for the first time since 1998.
The Rams defense held the nation's No. 10 offense in totals yards per game average in check and forced three turnovers.
Bibbs, whose previous career-high in rushing yardage was 147, had TD runs of 7, 59 and 9 yards on 29 carries. He averaged 6.9 yards per rush.
Grayson completed 18 of 23 passes and had one interception. He was 15 of 18 in the first half when CSU gained a 24-7 lead. He completed TD passes of 24 yards to Kivon Cartwright, 22 yards to Austin Gray and 34 yards to Donnell Alexander.
Brett Smith led Wyoming, completing 21 of 36 passes for 246 yards and a touchdown.
Dominic Rufran caught seven of Smith's passes for 135 yards, including a 71-yard score.
CSU dominated the game from the outset, gaining a 21-0 lead as the Rams offense shredded the Cowboys defense for 289 total yards and averaged 6.4 yards per play in the first half.
By contrast, Wyoming's offense, which entered the game averaging 518.8 total yards a game, struggled. At one point early in the second quarter, CSU had outgained the Cowboys in total yardage 220-34.
Smith, who entered the game ranked third in the nation with an average of 379 total yards a contest, had just 78 passing and rushing yards in the half.
The Cowboys ended the game with 416 total yards.
CSU, which was averaging 403.3 yards a game, finished with 509.
Under Armour Youth Colorado State Rams #18 Green Replica Football JerseyPrice: $55.00 Shop
What we're thankful for in the Pac-12 this season, including an influx of young talent, surprises both good and bad, and the College Football Playoff.
Clemson defensive coordinator Brent Venables and Alabama defensive coordinator Kirby Smart are among the 34 nominees for this year's Broyles Award.
Welcome to an early Thanksgiving edition of the Big 12 Twitter mailbag, which includes plenty of playoff talk.
Skyler Howard has tuned out the criticism and focused on his team, and the Mountaineers have turned things around.
The Cardinal quarterback will face the Irish for the last time Saturday after converting his entire family to Stanford fandom.
Wisconsin coach Paul Chryst talks about the team's loss to Northwestern and what QB Joel Stave's legacy will be when he leaves the Badgers.