Krasnodar, who were taking on German opponents for the first time, started off the stronger side with attacking threat having had two shots on goal within the opening stages.
Mauricio Pereyra had an early chance to break the deadlock, but his effort missed the target, and minutes later ex-Chelsea player Kevin De Bruyne had a chance of his own that went missing.
The away side grew into the half and were rewarded in the 37th minute when the ball scrambled over the net following a touch from Krasnodar's Andreas Granqvist after goalkeeper Andriy Dykan failed to safely clear the danger following De Bruyne's shot.
Krasnodar were still in with a chance of getting something out of the game as the first half came to an end, but after the interval they were dealt an early blow when De Bruyne got himself on the scoresheet.
Just 39 seconds after the restart, De Bruyne cut in from the right to latch on to a pass from Naldo and drilled the ball into the back of the net.
The home side were given a slice of hope in the 50th minute when the referee awarded Krasnodar with a penalty after Naldo handled in the area, which allowed Granqvist to redeem himself and knock the ball into the top right corner and narrow the deficit.
The Russian team had a burst of energy after getting a goal back and tried to search for the equaliser, but Wolfsburg pushed them back again by stretching their lead.
Some individual brilliance came from Brazilian midfielder Luiz Gustavo, who unleashed a swerving shot, which dipped behind the keeper and below the bar to give the German outfit a 3-1 lead.
De Bruyne added to his goal tally with 10 minutes left to play, and Wanderson managed to get on the scoresheet for the home side in the 86th minute, but Krasnodar were left with too much to do in order to gain anything out of the contest.
As it stands, Wolfsburg sit second in Group H, one point below leaders Everton, while Krasnodar sit at the bottom with two points from three games.