But Fernandes followed with Russia's second miss of the shootout.
Croatia, a shadow of the team which cruised through their group with maximum points, won the shootout when Ivan Rakitic calmly netted and they will face England in the semi-finals in Moscow on Wednesday.
Denis Cheryshev got Russian Federation off to a brilliant start by marking his return to the starting line-up with yet another contender for goal of the tournament after his stunning efforts against Saudi Arabia and Egypt in the group stage, but Andrej Kramaric equalised just eight minutes later.
Croatia continued to dominate possession and Krammaric had the first shot of the second half, acrobatically volleying Vrsaljko's cross straight into the waiting hands of Akinfeev.
Rare chances for Stanislav Cherchesov's team saw Dzyuba head tamely at Danijel Subasic from a 62nd-minute corner, before substitute Aleksandr Erokhin sent his header well over the bar from Fernandes' cross on the right 10 minutes later. Croatia's shooters did enough that Ivan Rakitic's successful penalty was the victor and set off another wild celebration with Subasic on the bottom of the pile.
Russian Federation recall Denis Cheryshev for their World Cup quarter-final clash with Croatia.
Modric said: "Our style was cramped a bit and maybe we did not want to risk with passes, so we had to balance it out in the second half".More news: At least one killed in Virginia helicopter crash
Russia goalkeeper Igor Akinfeev, left, reacts as Croatia players celebrate after scoring the winning penalty during the quarterfinal match between Russia and Croatia at the 2018 soccer World Cup at the Fisht Stadium in Sochi, Russia, Saturday, July 7, 2018. "We gave everything we could".
Argentina in 1990 had been the last team to win consecutive World Cup shootouts.
Fernandes, who scored the equaliser for the Russians, fired dreadfully wide and despite successful spot-kicks from Sergei Ignashevich and Daler Kuzyayev, Russia knew that if Ivan Rakitić scored they would be eliminated. This was not a attractive game, it was a fight, a battle for the semifinal.
"I don't cry often, but now I have good cause", said Croatia coach Zlatko Dalic. "We were lucky. I was concentrating throughout the match, but after that penalty it came bursting out of me".
Croatia came within an inch of taking the lead on the hour mark as Akinfeev tried and failed to reach a Mandzukic cross, and the ball fell to Ivan Perisic, who tried to aim a shot inside the post only to see it come off the woodwork and roll through the six-yard box untouched. Quickly eyeing the open space on his right, he played a give-and-go with Dzyuba to create space, and then unleased a left-footer to the awe of all who witnessed a classic goal.
Both teams are coming into the World Cup with thrilling victories in the quarter finals against Spain and Denmark respectively.