Ivan Rakitic stroked home the winning penalty to send Croatia into a semi-final against England after a night of unremitting tension in Sochi, ending the remarkable campaign of a team ranked 70th in the world.
Russian Federation had opened the scoring in the 31st minute, courtesy a spectacular long-range effort from winger Denis Cheryshev which sent the home fans into delirium.
After making the semi-final in 1998 in France the Croatians return to the last four, this time to face England.
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.More news: Gareth Southgate says England are well-prepared to face Tunisia
Croatia goalkeeper Danijel Subasic was issued a warning by Federation Internationale de Football Association after his team's World Cup victory over Denmark for revealing a T-shirt with a message honouring a former teammate who died a decade ago from injuries suffered during a match.
The following time in the first half saw the referee booking two Croatian players.
This was the first time since 1994 that a team tied a match after going behind in extra-time.
Andrej Kramarić's goal against World Cup hosts, Russia.More news: Lions eat 'rhino poachers' on South African game reserve
Domagoj Vida made it 2-1 for Croatia 10 minutes into the second stanza with a fine header that sailed into the bottom corner.
It was the second straight time both teams played in a shootout. Igor Akinfeev later blocked an attempt from Mateo Kovacic.
Ivan Rakitic scored the victor from the spot as Russian goalkeeper Igor Akinfeev dived the opposite direction.More news: Thai coach apologizes to parents as boys write they're OK