Croatia won 4-3 on penalties, knocking the host nation out of the tournament after both Fyodor Smolov and Mário Fernandes miss the net.
Denis Cheryshev's swerving left-footer from the edge of the box had opened the scoring for Russian Federation in the 31st minute of normal time but an unmarked Andrej Kramaric headed in a cross from Mario Mandzukic eight minutes later to restore parity.
While Russia also started well in Saturday's energy-sapping quarter-final duel against Croatia, they ran out of steam and ended bowing out against the Luka Modric-led side. Vida makes it 2-1 in the 100th minute.
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 sent a courageous Denmark side home via penalties too last Sunday.
Facebook: 800K users may have had bug unblock blocked people
While Facebook found a solution for the problem, it doesn't raise confidence in the company's ability to keep its user data safe. Due to what it's calling a bug, the social giant says it temporarily unblocked some users that had been previously blocked.
Then in 1990 in Italy they beat Cameroon in extra time to head into another semi-final, this time they faced Germany and lost on penalties, the beginning of their long hoodoo from 12 yards.
With just six minutes left of extra time Fernandes headed the hosts level from a free kick on the edge of the area after a handball and the game went to penalties.
After a pair of the quarterfinal matches played on Friday, team France enjoyed a confident defeat of 2-0 over Uruguay in the city of Nizhny Novgorod, while Belgium went for 2-1 win over the legendary Brazilian team in the city of Kazan.