Lionel Messi scored from the penalty spot inside five minutes and Gerard Pique headed home to secure an unconvincing victory.
Messi is yet to score a goal from open play this season.
A consolation tap-in goal was a deserved reward for a spirited performance from Kyiv.
Dynamo Kyiv fielded a significantly depleted side, with only 13 first-team players traveling to Spain along with a further six youth players. Six players had tested positive for coronavirus at the Ukrainian club before the tie.
It was an uncomfortable night for Barcelona, who struggled to assert themselves in the second half despite enjoying the lion's share of possession.
A valiant performance from 18-year-old Kyiv goalkeeper Ruslan Neshcheret on his first-team debut ensured the goal deficit was held to just one.
Barcelona dominated for the opening 20 minutes and it seemed it would be a routine performance for Ronald Koeman's side, who have struggled to find form in La Liga but won both of their other group matches in Europe comfortably.
Kyiv were tenacious and captain Viktor Tsygankov's 75th-minute goal made for a nervy finish to a tricky night for Barca, who looked ill at ease for large periods.
Goalkeeper Marc-Andre ter Stegen was involved more than expected between the Barcelona sticks as he made his first appearance since recovering from a knee injury.
Kyiv face another challenge in their next match in the Ukrainian Premier League against Shakhtar Donetsk.
Messi - trouble in front of goal?
Barcelona's star man Messi has failed to score from open play so far this season, despite featuring in every match for the Catalan side.
In fact, Messi has registered just one goal in six La Liga matches, a penalty against Villarreal. A considerable drought for someone who has scored 445 goals in his 16-year Barcelona career.
It has been a turbulent few months for the Argentine after handing in a transfer request hoping to leave the Nou Camp, culminating in some unpleasant rumors and the eventual decision to stay at the Spanish giants.
Granted, Barcelona are going through a period of change and it is not just Messi who is struggling to find form - Barcelona are 12th in La Liga with just eight points from six matches.
But the 33-year-old forward can often be relied upon to provide a moment of 'Messi magic' just when it's needed - something which, this season, he has so far been unable to do.
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