Martin Braithwaite would add a brace after Dest's goal before Antoine Griezmann wrapped up a comfortable win that saw the Catalans advance to the last 16.
Dest's goal meant he became the first American to score in the Champions League for Barcelona, in a match when his USMNT team-mate Konrad de la Fuente also made his senior debut for the Catalans.
After the game, the 20-year-old couldn't help but express his satisfaction with his and his team's performance on the evening.
"It's a perfect day, I'm very happy to score my first goal, the team has played very well and I think we have done a great job," Dest said.
"I am the first American to score in the Champions League with Barca, it is a source of pride and even more so doing so with a club as important as Barca."
Playing as a right-back, Dest got forward every opportunity he could against Dynamo, which he did effectively to take the ball off Braithwaite in the box and finish low into the corner for his goal.
The USMNT defender said that playing on the front foot was part of his side's game plan on the night.
"The game needed to play like this and I have done so, to look for the rival goal," Dest said. "It is an important victory for us, we are in a good position in the Champions League."
With Sergi Roberto facing two months on the sidelines due to a thigh injury, Dest could be set for an extended run in the team. Still, he expressed his disappointment that his team-mate will likely be out until 2021.
"I do not like that Sergi Roberto is injured," Dest said. "I wish him a quick recovery. Now I have the opportunity to play and I will try to do my best."