The meeting at the Bolshoi Stadium ended with a score of 2:3.
As part of the Sochi club, Yuri Alexandrov and Matvey Michkov distinguished themselves.
At the Moscow Region team, goals were scored by Scott Wilson, Vladimir Galuzin and Ivan Yezhov.
Sochi became the first team in KHL history to lose 20 games in a row.
The previous anti-record belongs to Spartak in the 2013/14 season.
Sochi (18 points) is 11th in the Western Conference standings.
Vityaz (54 points) is in sixth place.
Earlier, the capital's Dynamo snatched a victory from Salavat Yulaev in the end of the KHL match.