Ansu struck the winner in the 70th minute in Kiev, smashing the ball into the roof of the net after Oscar Mingueza's cross had been deflected into his path.
The win takes Barca onto six points from four games, six behind Group E leaders Bayern Munich but two clear of third-place Benfica, who they host at Camp Nou later in November. A win will book their place in the round of 16.
As Barca wait to appoint club legend Xavi Hernandez as their new coach, the result was always more important than the performance in Kiev on Tuesday. Interim boss Sergi Barjuan's side did just enough to ensure they returned to Barcelona with three points. After losing their first two games in the Champions League this season, they're now in a great position to ensure they're still playing top-level European football in 2022.
Ansu, who turned 19 two days ago, was once again the other positive. The forward missed Barca's last two matches with an injury but returned to score the vital goal in Ukraine, even though he wasn't at his brilliant best. Ousmane Dembele's latest return from injury and a clean sheet also represented good news.
Despite beating Dynamo in the end, Barca's lack of goals is a concern; Ansu's effort was their first away from Camp Nou since August. In total, they've only scored twice on the road this season in addition to just two goals in four Champions League games.
Manager rating out of 10
6 -- Barjuan earned his first win as interim boss but it's hard to say he's changed the team too much from the Ronald Koeman era. One thing he did do differently was not sit back once Barca took the lead.
Player ratings (1-10; 10 = best, players introduced after 70 minutes get no rating)
DF Oscar Mingueza, 6 -- A lot of Barca's attacks ended with the defender crossing from the right side. The majority failed to create any danger but one did lead to Ansu's goal.
DF Eric Garcia, 6 -- Managed the game well after getting an early booking. A bit slow on the turn at times.
DF Clement Lenglet, 6 -- Held his position well defensively and was good on the ball. Hit the post in the first half, although it would not have counted as the flag went up.
DF Jordi Alba, 6 -- Offered an outlet on the left but his final ball let him down.
MF Sergio Busquets, 6 -- Cut out several Dynamo attacks and encouraged Barca to press high.
MF Nico Gonzalez, 7 -- Another really good performance from the 19-year-old, whose bounced back well from being taken off at half-time against Atletico Madrid one month ago.
MF Frenkie de Jong, 5 -- Didn't look 100% after rushing back from a hamstring injury to start the game.
FW Gavi, 6 -- Moved to the right wing to accommodate for the loss of Dest. Had a couple of nice moments but is better through the middle.
FW Memphis Depay, 6 -- Missed the chances which came his way, with one blocked in the opening three minutes and another saved late on. Inadvertently blocked a Nico header which was goal-bound, too.
FW Ansu Fati, 7 -- Barca must keep their best finisher fit. Took his goal so well, which shouldn't be surprising given it's his third since he returned from 10 months out with a knee injury.
FW Ousmane Dembele, 6 -- The French winger returned from four months out with a bright and pacey performance. Could be a real boost for Barca in the coming weeks.
DF Ronald Araujo, NR -- Returned from injury to make his first appearance in a month, taking the place of the injured Lenglet.
FW Alejandro Balde, NR -- The left-back replaced Ansu for the final five minutes.