Krasnodar celebrated the eighth anniversary of their founding by eliminating Fenerbahce and reaching the last 16 of the Europa League for the first time thanks to a 1-1 draw that secured a 2-1 aggregate triumph.
Dick Advocaat's Fener lost the first leg 1-0 in Russia and found themselves with an even tougher task after just seven minutes in the return match as Fyodor Smolov found the bottom-right corner from 20 yards following a defensive mix-up.
Fener piled the pressure on at times and did level just before the break through Souza's close-range finish after a set-piece caused havoc in the area.
But the hosts failed to complete the turnaround and Krasnodar, who were only founded on February 22 2008, scraped through to second knockout phase.
Joining Krasnodar in the next round will be Schalke, who ultimately coasted past Greek side PAOK 4-1 on aggregate after a 1-1 draw in Gelsenkirchen.
Alessandro Schopf put them ahead 23 minutes in with a simple finish and, although Matija Nastasic scored an own-goal shortly after to level things up on the day, the Germans never looked in danger of throwing the tie away.