Ivan Rakitic got what could prove a vital second against his old club late on, but plaudits on the night belonged to the Frenchman Kounde.
The 22-year-old ran from his own half to fire Sevilla in front with 25 minutes gone, evading several challenges before burying a shot beyond Marc-Andre ter Stegen.
Barcelona piled on the pressure in the closing stages but could not find an equaliser before Rakitic finished off a counter-attack for Sevilla with five minutes left – offering Julen Lopetegui's side something of a cushion going into the second leg at the Nou Camp on March 3.
Barca had started positively, with Lionel Messi forcing a save from Bono in the 11th minute after being teed up by Antoine Griezmann.
The Argentinian sent another opportunity over in the 22nd minute, but it would be Sevilla's young centre-back who would steal the show moments later.
Kounde was in his own half when he first picked up the ball, quickly exchanging passes with Suso as he began to edge forward, slowly at first but with ever more conviction as he skipped past challenges with space opening up in front of him.
He arrived in the box with only Ter Stegen to beat and made doing so look easy as he rifled the ball into the bottom left corner.
Barcelona sought an immediate response but Messi sent a free-kick straight at Bono.
Sevilla did an effective job at stifling their visitors for the remainder of the half, which ended with the hosts back on the attack as Sergio Escudero's shot was saved by Ter Stegen.
Barca were back on the attack early in the second half, but Messi's shot was blocked before Jordi Alba fired high and wide.
Sevilla twice went close on the hour mark as Rakitic and Diego Carlos both saw shots blocked.
Luuk de Jong and Munir El Haddadi were part of a triple Sevilla substitution with 20 minutes to go as Lopetegui sought to build on Sevilla's advantage, but it was Barca who turned up the heat.
Messi fired narrowly wide before Ousmane Dembele was twice denied and Junior Firpo saw a header blocked.
But with Barca pushing forward they left the door open at the back.
A long ball forward found the run of Rakitic down the left, and the Croatian took it in his stride before cutting in and firing into the roof of the net.
Messi had one more chance in stoppage time but Bono was again equal to his shot as the night ended in frustration for the Catalans.