Manager Ronald Koeman's side have moved off the bottom of Group E, claiming their first win in the competition following four defeats in their previous five Champions League games in a run that stretched back to December 2020.
Right-back Sergino Dest looked to open the scoring with a one-on-one chance on 35 minutes but fired a down the throat of Dynamo goalkeeper Heorhiy Bushchan. However, shortly after the ensuing corner, defender Gerard Pique volleyed home a floated cross from left-back Jordi Alba -- Barca's first goal of this season's competition after suffering back-to-back 3-0 defeats to Bayern Munich and Benfica in their opening two matches.
Forward Ansu Fati looked to double Barca's lead early in the second half when he stole the ball away from Bushchan near the goal line before attempting a standing-overhead kick that sailed over the bar.
The hosts rarely looked troubled in the tie, dominating possession without conceding a shot on target.
Alba sustained an ankle injury in Wednesday's match and could miss the game against Madrid, saying he felt "excruciating pain" during the second half.
"I don't know what it is but I have something. I'm hurt," Alba said.
"It's an important week for us, we won two games in a row and losing against Dynamo would eliminate us from the Champions League. Now it's El Clasico and it will be tough, we need our supporters to be on our side."
Information from Reuters contributed to this report.