With 79 minutes on the clock, reigning champions Argentina were 2-0 down to Egypt and looking like they were about to be eliminated.
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Defender Cristian Romero then pulled one back before Lionel Messi scored the equaliser just four minutes later.
Argentina kept pushing for the winner and then a lovely looping cross from Lautaro Martinez landed perfectly on Fernandez head, nodding home the winner.
Speaking to journalist Gaston Edul after the game, the 25-year-old said: "I've just scored the goal of my life. We were on the ropes and we pushed forward with everything we know. We're a team with heart."
Fernandez and co will now face the winner of the Switzerland vs Colombia game in the quarter final on Saturday (July 11).