Croatia sent a courageous Denmark side home via penalties too last Sunday.
They have quickly been embraced as national heroes, with the mayor of Moscow responding by making additional public viewing space available in the city before the match in Sochi's Fisht Stadium.
Eight minutes (and two yellow cards) later Croatia responded with a 39-minute goal from Andrej Kramarić.
It was a dramatic end to the match for Subasic who went down with what appeared to be a hamstring injury late in regulation time. The English team defeated Sweden 2-0.
It was the second straight time both teams played in a shootout.
Croatia goalkeeper Danijel Subasic made one save in the shootout, blocking Fedor Smolov's attempt. Igor Akinfeev later blocked an attempt from Mateo Kovacic.
The overachieving hosts, the lowest ranked nation in the tournament, were trying to make it to the World Cup semifinals for the first time since the Soviet Union team finished fourth at the 1966 tournament in England.
Full Time: Russia 1 vs Croatia 2 - Kramaric cancelled out Cheryshev's opener in the first half and there were no goals in the second half.
Ivan Rakitic has expressed his shock at seeing former Barcelona team-mate Andres Iniesta left out of Spain's line-up for their final World Cup match, saying the omission "hurt a lot".