With less than a minute left and hosts Alania leading 3-1, the game was halted as dozens of people including substitutes, coaches and security personnel ran on to the pitch.
Players grabbed each other by the throat and there was lots of elbowing, pushing and shoving.
The referee stopped the match for almost 10 minutes before order was restored. He then sent off one player from each side and booked four others.
"You could see the emotions of both teams running so high. For both clubs it was like the last chance, a fight to the finish," said Premier League chief Sergei Chaban.
"We'll make sure the guilty people are punished."
Alania eventually won 3-1 to move level on 16 points with second-from-bottom Mordovya with six games to go.
The bottom two go down and the next two clubs take part in a relegation play-off.