In a first half of few chances, the hosts went in front thanks to a thunderbolt from Denis Cheryshev, who curled home into the top-corner in the 31st minute.
Domagoj Vida headed Luka Modric's corner home 10 minutes into the first extra period, only for Fernandes, the Brazil-born defender who was only granted Russian Federation citizenship by president Vladimir Putin two years ago, to keep Russia's hopes alive in a dramatic finish.
With the sheer amount of firepower Croatia has in their frontline, it could fall upon Russian captain and shootout hero Igor Akinfeev to send Sbornaya through to the semi-finals and continue their strong run. Kramaric headed home the offer from the forward, beating Akinfeev for the first time in regulation.
Ante Rebic used a fine turn in the box to take a shot from a tight angle that was pushed aside for a corner, from which Rebic headed over the bar.
Ivan Rakitic is your man!
Despite having home advantage, Russian Federation slumped to a 3-1 against Croatia in November 2015 to hand them their first loss between the two sides.
Then goalkeeper Danijel Subasic pulls his hamstring but Croatia had already used up all three substitutes allowed for normal time. Croatia equalized with Andrej Kramaric's header near halftime.
Kramaric threatened again seven minutes into the second half, although his overhead-kick was comfortably claimed by Akinfeev, who saw Ivan Strinic fire well over the crossbar from 22 yards out on the left in the 58th minute, before the woodwork came to Russia's rescue two minutes later.
Both sides were probing for the second goal in the closing minutes of the first stanza, but they went into the dressing room deadlocked at 1-1.
After Fernandes' failure, Modric got lucky when his strike found the net following touches off Akinfeev's glove and the post.
But nearly immediately after making their third sub in the 88th minute, Subasic fell to the pitch grabbing his hamstring, and he was forced to continue after receiving treatment and made a save at his near post.
The game stayed locked at 1-1 through the final whistle, prompting two periods of extra time.
And nearly immediately afterward, Croatia had their victor.
Subasic saved the first attempt of the shootout when he made an adjustment while diving to get a hand on Fyodor Smolov's attempt.
However, the 90 minutes would produce no more goals, with the game forced into extra-time.
Smolov began the shootout by sending a soft shot that Subasic was able to paw down after diving to his right, and Brozovic put Croatia ahead. Akinfeev denied Mateo Kovacic and nearly kept out Luka Modric's effort from 12 yards out, but Rakitic converted the decisive effort to seal a 4-3 win in the shootout.