The La Liga giants made it four wins out of four Champions League games with an emphatic victory at the NSC Olimpiyskiy.
After a tepid first half were both teams lacked the guile and imagination to break the deadlock, Barcelona found their mojo after the break as Sergino Dest got the first goal of the game seven minutes into the second half.
Martin Braithwaite got the visitors’ second five minutes later before scoring again from the penalty spot on the 70th minute mark.
Substitute Antoine Griezmann got his name on the scoresheet deep into injury-time to compound the hosts misery.
"We have achieved our goal, qualify for the eighth. The image has been very positive. The team has put a lot of energy. There was a lack of effectiveness in the first half, but in the second we dominated and we had a good game,” Koeman told Marca after the game.
“The result is to be happy. . I liked the collective performance. They have worked hard, they pushed. The image given today is the one we want to give. All the players have been hungry. The youngsters and all have given a good image and the result is good.
"We have seen a very hungry team. We scored four goals, important players were able to rest and the youngsters have deserved these minutes. They have delivered. I highlight the whole team."
Next up for Barcelona is a trip to Pamplona to face Osasuna at the El Sadar Stadium on Sunday.
