The main time of the meeting, held in Grozny, ended with a score of 2:2.
At the 55th minute, Batraz Gurtsiev led Vladikavkaz forward.
The blue-white-blues responded with goals from Yuri Alberto and Ivan Sergeev in the 71st and 82nd minutes.
In the third stoppage minute, Nikolai Giorgobiani, with a magnificent free-kick, again restored equality and turned the game into a penalty shootout.
In the 11-meter series, the hosts' players turned out to be more accurate - 6:5.
The decisive goal was scored by Alan Khugaev.
Thus, the wards of Spartak Gogniev made it to the semi-finals of the tournament.
The draw for the next stage will take place on 21 April.
Earlier it was reported that Yenisei defeated Rubin and reached the semifinals of the Russian Cup.