The Vatreni held their nerve from the spot following a 2-2 draw after extra time to reach the last four for a second time.
Relive how the dramatic contest unfolded with Sports Mole's live text coverage below.
STARTING XI: Akinfeev; Fernandes, Kutepov, Ignashevich, Kurdjasov; Samedov, Kuzyayev, Golovin, Zobnin; Cheryshev; Dzyuba
SUBS: Semenov, Gazinskiy, Dzagoev, Smolov, Lunev, Granat, Al. Miranchuk, An. Miranchuk, Zhirkov, Gabulov, Erokhin, Smolnikov
STARTING XI: Subasic; Vrsaljko, Vida, Lovren, Strinic; Rakitic, Modric; Rebic, Kramaric, Perisic; Mandzukic
SUBS: Livakovic, Corluka, Kovacic, Brozovic, L.Kalinic, Jedvaj, Bradaric, Caleta-Car, Badelj, Pjaca, Pivaric
Stanislav Cherchesov: "As a coach I am trying not to watch the TV, I don't read papers, I am concentrating on my job. I believe that is the same for the players. I am trying not to get distracted. If I get a newspaper I will read a headline. Criticism is good but I believe we should have our eyes and ears open. We Russians like extremes so let's not go to these extremes. I believe it should be constructive, analytical criticism. You say people are euphoric: we, the people in the team, are not the people who should be euphoric."
Zlatko Dalic: "We cannot choose our opponents, hosts or otherwise. We are facing a huge game in the quarter-finals and it doesn't matter who the opponents are. The only difference is they will have vociferous fans but every week our team plays with opposing fans howling at them. It shouldn't be a problem. We will not be looking for excuses. We have to play our own game regardless of who is in the stands."
RUSSIA SUBS: Semenov, Gazinskiy, Dzagoev, Smolov, Lunev, Granat, Al. Miranchuk, An. Miranchuk, Zhirkov, Gabulov, Erokhin, Smolnikov
CROATIA SUBS: Livakovic, Corluka, Kovacic, Brozovic, L.Kalinic, Jedvaj, Bradaric, Caleta-Car, Badelj, Pjaca, Pivaric