Roberts' boot capped a comeback in which the Rams (8-6) reeled off 18 points in a 2:52 span down the stretch to rally from 45-30 deficit, aided by three Washington State turnovers.
Kapri Bibbs rushed for 169 yards with three touchdowns on 27 carries, including a 1-yard run with 33 seconds left that pulled Colorado State within two at 45-43.
Donnell Alexander dove to hit the pylon in the corner of the end zone on the ensuing 2-point conversion, forging a tie.
The Cougars' Teondray Caldwell fumbled the ensuing kickoff, setting up Roberts' game-winning kick.
Garrett Greyson completed 31-of-50 passes for 369 yards, two touchdowns and an interception for CSU, which rolled up 595 yards of total offense.
Connor Halliday went 37-of-58 through the air for 410 yards and a career-high six TD passes with an interception for Washington State (6-7).