Denis Cheryshev had put Russian Federation in front in the 31st minute with a superb strike - his fourth goal of the tournament - but that was cancelled out eight minutes later by Andrej Kramaric's header.
But then, with just five minutes to go, Mario Fernandes played the role of hero, heading home a set piece to make it 2-2.
After Russia's blistering start, Modric-led Croatia gradually controlled the ball and the first half saw 65 percent ball possession for Croatia. It was, however, the Croatians who continued in the competition with a second penalty win.
115 - Goal! Russia 2, Croatia 2.
Luka Modric is the team's star but it is goalkeeper Subasic who got them past the finishing line against Russian Federation.
39 - Goal! Russia 1, Croatia 1. Assisted by Mario Mandzukic.
The hosts continued to put Croatia's defense under pressure but the Modric-led team kept their cool and equalized in ice-cold fashion six minutes from halftime through Andrei Krammaric. Denis Cheryshev (Russia) left footed shot from outside the box to the top left corner. But they delivered some great results, most notably dumping Spain out in the last 16, and players like Cheryshev, Artem Dzyuba and Akinfeev all did their reputations a power of good.
Russia & Croatia face off in Sochi with a place in the final four on the line.
"We should have finished the job before penalties, but maybe it's written in the stars that we have to go through the extra drama", said inspirational playmaker Luka Modric.
He spent nearly two years out of global football following Russia's group stage exit from the 2016 European Championship but made a surprise return to the national squad in May. It became 1-1 when Alan Dzagoev scored and Mateo Kovacic flopped.
Russia's Yuri Zhirkov's experience will be missed today as the defender will sit out the game due to a calf problem.
Croatia also progressed to the quarter-finals thanks to a penalty shoot-out victory over Denmark.
Instead the opener came at the other end three minutes later from Sbornaya's second foray into the final third.
Dalić may consider tweaking his side slightly for the game against the host nation.
"We have two matches to play, we are very motivated, we will give our all".
With a penalty shootout looming, there was concern for Croatia as Subasic appeared to be struggling with cramp.
England, France and Belgium have booked their places in the semis so there's only one spot remaining and Croatia and Russian Federation will fight for it tonight. The victor of that game faces England or Croatia in the 2018 World Cup final.