Barcelona manager Ronald Koeman fielded a team without talisman Lionel Messi and midfielder Frenkie de Jong, with both players staying behind in Spain to rest because of a club and country fixture pileup in recent weeks.
The Catalans seemed to miss Messi in the final third, as they dominated possession throughout a scoreless first half but never created any legitimate scoring chances.
However, the visitors found themselves in front when Dest, the first American to play for Barcelona, finished smoothly following a nice interchange with Carles Alena and Martin Braithwaite to put his side up 1-0.
The goal makes Dest the 10th U.S. international to score a goal in the Champions League.
"Really happy to score my first goal. Overall, we played good as a team, everybody played good, and we took the win," Dest said after the match.
"We have two more games to go, but we're in a good position right now. I am fairly happy that we won, and I can't wait for the next game.
"I'm really happy to score my first goal. I think we needed a goal. It was an important one, to score the 1-0. Hopefully many more to come."
Braithwaite doubled the advantage minutes later when he poked home at the far post from a flicked-on Oscar Mingueza header following a corner to pad the Catalans' lead.
Gerard Pique's serious knee injury in the weekend's loss against Atletico left Barca with only one fit central defender, and Koeman was forced to turn to 21-year-old Mingueza, who began the season in the club's reserve side.
Barcelona's third came once again courtesy of Braithwaite, who fired in his second of the night from the penalty spot around 70 minutes to secure his team's fourth win from four in the Champions League.
Konrad is the seventh U.S. international to appear in the UCL this season, breaking the record of six set in 2004-05.
Of his Barca debut, Konrad said: "Incredible feeling making my debut and also my Champions League debut. I am thankful for everyone that helped me get here, and I will continue to work hard and hopefully get more chances.
"I am really happy. I have worked hard from a very young age for this moment, and I finally got a chance."
Substitute Antoine Griezmann added further gloss to the scoreline with a goal in stoppage time.
With the win, Koeman's side are assured a spot in the round of 16 for the 17th consecutive season and have a good shot at winning Group G ahead of second-placed Juventus.
"We've completed our objective, which was to qualify, and we gave a very positive image of ourselves," Koeman said.
"We played with a lot of energy, and although we were not very effective in the first half, we dominated the second and had some very nice passages of play.
"Every player showed hunger, and the young players gave good displays, too."