Ivan Rakitic stroked home the winning penalty to send Croatia into a semi-final against England after Mario Fernandes dramatically equalised for Russian Federation with five minutes of extra time remaining, only to miss a crucial kick in the shootout.
However, it was not to be for the resilient hosts, with goalkeeper Danijel Subasic saving Fedor Smolov's penalty and Fernandes firing wide before Rakitic kept his composure to send Croatia through.
Croatia were stunned. But the Russian lead had lasted only eight minutes before they drew level, Mario Mandzukic cutting the ball back for Kramaric to head home.
Following a long ball forward, Cheryshev gathered and played a one-two with Artem Dzyuba to get around Luka Modric, then stepped up to launch a shot from 25 yards into the top corner, leaving Croatia keeper Subasic stranded.
Croatia will face England on Wednesday, July 11th. Croatia equalized with Andrej Kramaric's header near halftime.
And it appears Dalic realised his mistake with extra-time looming as he brought Marcelo Brozovic on for Perisic midway through the second-half, switching to a 4-3-3 which gave both Modric and Rakitic a bit more freedom than they had been afforded and lead to the no.10's Man of the Match display.
For Croatia, Mateo Kovacic had his penalty saved, but Marcelo Brozovic, Modric and Vida all netted theirs before Rakitic stroked in the victor.
'After we went 2-1 ahead, we should have maintained our focus, but there was a lapse of concentration.
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.
Back up the other end, Mandzukic directed a header over from a 77th-minute corner in what was the final attempt in regulation time, but the first extra-time goal of the World Cup arrived on 100 minutes and it was Croatian fans celebrating.
And nearly immediately afterward, Croatia had their victor.
Croatia finally broke the deadlock in the 100th minute when Vida headed home from a Modric corner.
Subasic was then tested again in the second period of extra time when he was able to corral Daler Kuzyaev's half-volley from the edge of the box, then stretched to cut out a cross.
"We have always said we would take one game at a time and we can go on and create our own history". Akinfeev made one save during the shootout and almost had another on Luka Modric, but the shot deflected off Akinfeev's hand, off the post and into the net.
Host nation Russia's dream run at the World Cup will be put to the test against Croatia in the quarter-finals on Saturday - Here are the confirmed line-ups for both sides.
Having knocked out Spain on penalties in the previous round, Russia, 70th in the Federation Internationale de Football Association rankings, again defied the odds to take 20th ranked Croatia to a shootout with a 2-2 draw after extra time but on this occasion their marksmanship deserted them.