Butterfield knocked down all six of his free-throw tries and added six rebounds and five assists for eighth-seeded Utah State (18-13), which will take on the tournament's top seed San Diego State in the quarterfinals on Thursday.
Preston Medlin led the team with 17 points and TeNale Roland added 14 points on 4-of-5 shooting from 3-point range.
For ninth-seeded Colorado State (16-16), Dwight Smith poured in a game-high 21 points, Jon Octeus netted 19 and both players collected eight rebounds. J.J. Avila pitched in 10 points and Daniel Bejarano handed out six assists.
Neither team shot greater than 37 percent from the field in the first half and the game was knotted at 31 heading into intermission.
Colorado State took the lead on its first possession of the second half and extended its advantage to as many as 11 with only 2:40 left to play. The Aggies caught fire down the stretch, ripping off a 16-3 run over the final 1:24. Butterfield's game-winning free throws with 40 seconds remaining were part of an 8-of-8 showing at the foul line for Utah State in the final minute.
Utah State shot 11 of 21 from 3-point range on the afternoon, while Colorado State was only 3 of 17 from beyond the arc.