Chechen club Terek were hoping to qualify for the June 1 final to be played in Grozny but Pletikosa shattered their dreams in the shootout following a scoreless 120 minutes.
The Croatia international denied Igor Lebedenko and Oleg Ivanov while Rostov scored from all four of their kicks to join CSKA Moscow, Zenit St Petersburg and Anzhi Makhachkala, who reached the last four in contrasting fashion on Wednesday.
League leaders CSKA eased to a 3-0 win over second division side Yenisei Krasnoyarsk, while big spenders Anzhi beat Dynamo Moscow 1-0 after extra time and champions Zenit squeezed past Kuban Krasnodar 4-3 on penalties after another scoreless game.
In next month's semi-finals, Rostov take on CSKA and Anzhi, eyeing their first major trophy, face Zenit.
- Sports & Recreation
- Anzhi Makhachkala
- Zenit St Petersburg
- Igor Lebedenko
- Oleg Ivanov