UMass (0-2) finished with 371 yards and collected 23 first downs. The Minutemen also rushed for 125 yards and had two scores on the ground.
Frohnapfel connected on 20-of-38 for 267 yards with an interception and was sacked twice. Colorado quarterback Sefo Liufau, meanwhile, threw for 318 yards on 26-of-42 with three TDs and an interception.
Defensively, Jovan Santos-Knox finished with 12 tackles, a sack and two hurries for the Minutemen.
After an unsuccessful possession by each team, Frohnapfel led UMass to its first score of the game with an efficient 85-yard drive, culminating in a 14-yard fade route to Rodney Mills.
On CU's next possession, Liufau completed a swing pass to Shay Fields, who scampered down the right sideline on a 19-yard play to put CU ahead 10-7.
Oliver added a 47-yard field goal midway through the second quarter to extend the Buffalo lead to 13-7.
UMass regained the lead on Jean Sifrin's first career touchdown, as the junior college transfer hauled in a 12-yard toss from Frohnapfel. That and the Blake Lucas’ extra point put the Minutemen back on top, 14-13, with 6:07 left in the half.
Tony Jones capped an 85-yard drive with a 5-yard rush to swing the momentum back in the visitor's favor and a 20-14 lead late in the first half.
A Lucas 34-yard field goal to open the third quarter gave the Minutemen a boost and a 24-20 lead. Randall Jette then made the defensive play of the game for UMass, stealing the ball away from Fields and returning it 29 yards to the 2-yard line. The Minutemen needed just one play to take their largest lead of the game, 31-20, on a Jamal Wilson rush.
CU by moving 77 yards and using a 14-yard run by Christian Powell to cut the UMass lead to 31-27. They retook the lead on a 70-yard TD pass to Nelson Spruce as he got behind the UMass defense on scramble play.
The Buffs took their largest lead of the game at 41-31 with 11:16 to play when Spruce caught a 3-yard pass in the back of the end zone. CU benefited from a 33-yard Tony Jones run two plays earlier.
Marken Michel gave the Maroon and White some life with a 7-yard TD run on the jet sweep to pull UMass to within three with 2:55 remaining.
UMass will return to play next week when it opens s 2-game road trip at Vanderbilt. Kickoff at Vanderbilt Stadium in Nashville is set for Noon Eastern Time.