Denis Cheryshev fired the hosts into a 31st minute lead with a spectacular strike but Andrej Kramaric headed home to make it 1-1 six minutes before the half-time break.
Ivan Rakitic has waved off Andres Iniesta after the veteran's time at Barcelona although it was his exit from the World Cup that left the Croatian most vexed. The first was against Portugal in 1966 when they went on to win the tournament, hosted in England, they had to wait 24 years till they reached the final four again.
Headers from Harry Maguire, from yet another set piece, and Dele Alli took England through to the semi but they had to wait to find out who they'd face.
Russian Federation were awarded a free-kick after Josip Pivarić handles the ball and the World Cup hosts get their equaliser.
With the game going into extra time, the tension was higher expectedly.
The following time in the first half saw the referee booking two Croatian players.
During the group stage, Croatia won all three matches, including a 3-0 rout of Argentina, and finished top of Group D, before beating Denmark on penalties in the last 16. Akinfeev looked to have saved Luka Modric's penalty but it came back off the inside of the post and span back into the net in cruel manner.
Rakitic then scored his second penalty shoot-out victor in two games.
However, it was the Croatians who held their nerve in the shoot-out to triumph 4-3 and will now face England on Wednesday.
Croatia appeared to have the tie in the bag after Vida's extra-time goal until Fernandes rose to head in a free kick and send both teams to their second penalty shootout of the tournament.