Valentin Wegmann led a balanced scoring attack for the Swiss outfit with 15 points while Marcus Sloan contributed 14.
Three others hit double figures in points for Benetton.
The Ukrainian outfit, who were behind all the way, trailed 51-39 heading into the final quarter but made things interesting over the final 10 minutes.
Led by the inspired play of American guard Corey Santee, they cut the deficit 70-64 with 27 seconds remaining.
The visitors then allowed 18 seconds to go off the clock before fouling Benetton's Dennis Harrison, who missed two free throws.
Santee hit a three-pointer right at the end but it was too little, too late for Sumykhimprom.
Santee had a game-high 24 points in defeat, 12 of them in the final quarter.
Neither side had a chance of advancing to the next round before the game.
Benetton take on Lokomotiv Rostov in their final group contest on January 13 looking for their first away win while Sumykhimprom, who are now 1-4, travel to France to meet Cholet Basket.
Rimantas Endrijaitis, coach BC Sumykhimprom:
"Benetton played aggressively and got a lot of rebounds. We made a lot of turnovers (20). We needed a couple of minutes to get into the game. Benetton analysed our game well and knew how to play against us."
Marcus Sloan, Benetton Fribourg:
"I'm very happy. We had to win one game in the EuroChallenge. Our defense was good tonight. With each game it's getting better for me and the team."
Damien Leyrolles, coach Benetton Fribourg:
"It was an interesting game for me. We started out very well and played a very aggressive ball game. Every player was very concentrated and motivated. We played much better against Brian Greene."