Pique volleyed home Jordi Alba's cross in the 36th minute to register Barca's first goal of this season's competition and secure their first victory after 3-0 defeats by Bayern Munich and Benfica.
Ronald Koeman's team moved to third in the standings with three points, one behind Benfica and three adrift of the Germans ahead of their clash later on Wednesday.
Barcelona received another boost when striker Sergio Aguero came on as a substitute late in the second half and looked to have recovered from the calf injury he suffered in pre-season after signing from Manchester City.
The Argentina international should be in contention to play in Sunday's Clasico against Real Madrid.
It was not a convincing win for Barcelona against a Dynamo Kyiv team who offered little attacking threat and did not muster a single shot on goal.
Barca coach Ronald Koeman left Ansu Fati, Philippe Coutinho and Aguero on the bench ahead of the Clasico and Sergino Dest, who usually plays left back, was moved up to play alongside Luuk de Jong and Memphis Depay in attack.
After a couple of missed chances by Dest and De Jong, the crowd started booing the home team and Koeman showed his frustration on the sidelines by asking Fati and Coutinho to warm up after only 31 minutes.
Just before the Dutch coach was about to make the substitutions, however, defender Pique eased the tension with a cool close-range finish from Alba's cross.
Fati and Coutinho came on after halftime and Barca improved with 18-year-old Fati showing his quality and almost scoring a brilliant goal with a backheel.
Barcelona were unable to turn their possession into goals but they hung on to seal a vital victory.