Key Opta stats: - Russian Federation are the first host country to be eliminated at the quarter-final stage of a World Cup since Mexico in 1986.
Croatia's Marcelo Brozovic gave his team a lead by making his attempt from the penalty spot.
Boasting Davor Suker and Zvonimir Boban, Croatia stunned Germany 3-0 in the quarter-finals before falling to hosts France in the semis.
But as in the previous match against Denmark - which Croatia also won on penalties after an insipid 1-1 draw - all too often his team mates failed to do anything with them.
Speaking to ITV, former Croatia manager Slaven Bilic said winning the World Cup would be the greatest sporting achievement in the country's history, which he now rates as a third-placed finish at France 1998.
Croatia players celebrate winning the penalty shootout.
In a related incident, Federation Internationale de Football Association also issued a warning to Croatia goalkeeper, Danijel Subasic, who lifted his jersey to reveal a T-shirt commemorating a teammate who had died from game-related injuries in 2008. - Croatia have now had eight different scorers at the 2018 World Cup - only Belgium (nine) have had more.
"We took a hard route and we were unlucky, particularly in previous tournaments, especially the Euros".
Subasic appeared to sustain a hamstring injury when stopping a deflected Aleksandr Erokhin cross go out for a corner, though he recovered to bat away Smolov's drive from an acute angle in stoppage time.
If only Fernandes had scored in the shoot-outs like he did in the extra time, it may not have been heartbreak for the hosts. However, during the Euro 2008 qualifiers, Croatia twice beat England, including in a decisive game at Wembley when Steve McClaren's reign ended after a 3-2 loss that meant England missed the tournament.
"We're giving our all".
"He watched, he was rooting for the team". They are still great guys for us, they are heroes. "They were dying on the pitch, we are proud with them", Kremlin spokesman Dmitry Peskov is quoted as saying by Interfax.