Tonight's match in Thessaloniki was goalless for a long time, but in the 73rd minute the Russian guests broke the deadlock when substitute Igor Smolinkov's entry against Marcus Berg was guided into goal by Paok defender Giannis Michalidis.
The uphill was steep for the Greeks, but they still equalized quickly through Omar El Kaddouri.
But as soon as hope was aroused, it was extinguished again.
Krasnodar's Dutchman Tonny Vilhena shot in the post from a distance and then Remy Cabella was there and put in 2-1 for the Russians.
For Viktor Claesson, it was a good Wednesday when he was selected for the national team for the first time earlier in the day since the cruciate ligament injury.
Against Paok, he played, just like Marcus Berg, the entire match.
Kristoffer Olsson has recently become a father and was missing from the match squad.
Danish Midtjylland, with the Swedes Joel Andersson and Jens-Lys Cajuste, is also ready for the Champions League.
They beat Slavia Prague in the playoffs.
The group game will be drawn tomorrow and starts on October 20.