Argentina were just four minutes away (plus injury time) from crashing out of the tournament when Rojo steered a brilliant shot into the bottom corner.
Nigeria appeared to be earning the point they needed to make the last 16 thanks to a cooly struck Victor Moses penalty cancelling out Lionel Messi’s superb opener in the 14th minute.
But Rojo showed remarkable nerves of steel and technique to hit Gabriel Mercado’s cross first time into the net to send the Argentina fans wild.
All the pressure in the build-up to the game was definitely on Argentina. Talk of rifts in the camp between coach Jorge Sampaoli and his players have run rife during the tournament.
Knowing they needed a win to have any chance of progressing to the knock-out stage after picking up just one point from two games, the Argentina line-up was totally different.
The most notable absentees were Chelsea keeper Willy Caballero and Manchester City striker Sergio Aguero, perhaps for different reasons.
Caballero paid the price for his horror show in the 3-0 loss to Croatia last time out, while Aguero appeared to have been disciplined for publicly criticising Sampaoli after that second game.
There was a lot of speculation that Sampaoli had little say in the five changes made overall or the switch to a 4-4-2.
In contrast Nigeria named the same XI that impressed during the 2-0 victory over Iceland. Unfortunately for them, this match must have felt like it was being played in Buenos Aires, rather than on neutral territory in Russia.
For the vast majority of the crowd were all Argentina fans, making the kind of racket that would inspire any team to victory.
Nigeria appeared to freeze on the big occasion in the first half and Messi didn’t hesitate to capitalise.
Roared on by his beloved supporters and perhaps invigorated by Argentina legend Diego Maradona’s presence in the stands, Messi ran Nigeria ragged.
Former Chelsea midfielder Mikel John Obi did his best to intimidate him early on by blocking an early run with a crude challenge, but it had no effect.
Just seven minutes later, the Barcelona collected a fine pass from Ever Banega and smashed the ball into the top corner. The TV cameras cut away to the sight of Maradona staring up into the heavens as if it was a moment of divine intervention.
Apart from the sublime goal, Messi played one sublime pass for Gonzalo Higuain to run on to but his shot was saved by Francis Uzoho.
The Nigeria keeper then came to his side’s rescue again by tipping Messi’s fine free kick on to the post to ensure Argentina were only one goal up at the break. It was a key moment in the match.
For Nigeria came out a team re-energised after the break. Perhaps they needed a strong word or two from manager Gernot Rohr to spark them into life.
It also helped that they were awarded the spot kick for Javier Mascherano pulling back Leon Balogun at a corner, soon after the restart. It settled their nerves and dented the confidence of the Argentina players.
Suddenly Messi was being negated and the legions of Argentina fans became a hindrance rather than a help as they began to turn on their players with every misplaced pass or shot.
Looking dangerous on the counter attack, substitute Odion Igahlo missed a glorious chance to secure the win by dragging a shot wide with the goal at his mercy.
For a brief moment, it looked like Nigeria might get a second penalty when Marcos Rojo headed the ball onto his own hand, but referee Cuneyt Cakir rightly said no after watching a VAR replay.
Igahlo still had time to see another shot saved by keeper Franco Armani and it proved costly as Rojo made a dramatic late impact.
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