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.
Baylor has released five signees from its 17th-ranked recruiting class, including J.P. Urquidez, Kameron Martin and Donovan Duvernay. Sources said the others are Patrick Hudson and Parrish Cobb.
ESPN's Jared Shanker and Matt Fortuna join The Paul Finebaum Show to break down the Week One showdown between Ole Miss and Florida State.
Gary Shelton of the Saint Peters Blog joins The Paul Finebaum Show to discuss the renewed energy of Florida football programs.
ESPN's Chris Fallica joins The Paul Finebaum Show to preview the opening weekend of the college football season.
Michigan coach Jim Harbaugh says young players at his camps this summer have him convinced that football has a bright future.
GameDay 100: During the Chick-fil-A Bowl in 2013, Texas A&M quarterback Johnny Manziel manages to stay on his feet, scrambling to buy time to complete the touchdown against Duke.