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.
It seemed Croatia were cruising to the semis, but Fernandes ensured it were shootouts that decided the course of the game.
Croatia finished the 1988 World Cup third, after a 2-1 loss to France in the semi-finals. He was replaced by Vedran Corluka, the team's fourth substitution, meaning Croatia can't sub Subasic if the match goes to penalties.
Croatia players celebrate winning the penalty shootout.
As far as the game itself, watchers marveled at Croatian goalkeeper Danijel Subašić, who suffered an apparent hamstring injury yet kept playing.
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"Thank you for the honest, genuine emotions you gave us thoughout the World Cup", they wrote.
He said: "We feel like conscripts, when they come to just before they have done their two-year (national) service, like those a bit demoralised who wanted to stay in the army for some more time longer. Thank God everything is fine with him".
"I felt really relieved".
England have no such fitness concerns after coasting to a 2-0 quarterfinal win against Sweden in normal time in Samara, but manager Gareth Southgate does have tactical questions to answer before the Croatia clash. The host nation lost 4-3 the penalty shootout, which followed 2-2 draw in the regular and 30-minute overtime period.
For Russians, the sadness was mixed with pride on Saturday evening after their team - the lowest ranked in the tournament - was halted in its tracks to World Cup glory by Croatia in a dramatic quarter-final match. "We gave everything we could".
President Vladimir Putin did not attend the game, but watched remotely, saying the players were heroes despite the defeat and the country was proud of them, Kremlin spokesman Dmitry Peskov was cited as saying by Interfax. If they trusted us or not, we trusted ourselves.