Pique volleyed in a superb opener from Jordi Alba’s cross as the hosts found the net in Europe for the first time in more than four and a half hours.
Barcelona were comfortable, if not clinical, and success keeps their hopes of reaching the knockout stage alive.
They sit third, one point behind Benfica, who play Bayern Munich later.
Barcelona headed into this fixture on the back of 3-0 defeats by Bayern and Benfica, managing just one shot on target in total.
They had not failed to find the net in three successive European games since March 1988 in the Uefa Cup – and Pique made sure that unwanted feat would not be repeated.
It was the 34-year-old defender’s first goal of the campaign and a timely one for the hosts, who were on a run of 287 minutes without one in the competition and had been frustrated by Kyiv.
Sergino Dest earlier headed over and Ansu Fati wasted a good chance to double his side’s lead, before Sergio Aguero was brought on for his first Champions League appearance for the club.
But the best chance that fell the former Manchester City striker’s way in his 15-minute cameo was a speculative long-distance effort that struck a defender.
It means Barcelona head into Sunday’s El Clasico against Real Madrid at the Nou Camp on the back of successive wins this week, having beaten Valencia 3-1 at the weekend.