Messi's first goal of the tournament got the two-time winners off to a ideal start in Saint Petersburg, but Victor Moses's 51st minute penalty had Jorge Sampaoli's men headed for a humiliating group stage exit until Rojo's late intervention.
"I don't remember such suffering", said Messi when asked if it was the most tense match of his career.
It nearly doesn't matter.
The Asian side faced an angry backlash for running down the clock in the last 15 minutes even though they were losing 1-0 on Thursday, gambling that Senegal would not equalise against Columbia in the other Group H game.
Messi had put them ahead in the 14th minute, with a fabulously taken goal but the Africans equalised through a Victor Moses penalty in the 51st minute. I don't know if you kept it or threw it away. We knew it was going to be a hard afternoon, but fortunately we have achieved our aim.
Nigeria needed at least a draw from the match to progress to the knockout stages of the Russian Federation showpiece, while the Argentines needed a win.
"It is a young team, though, and in four years most will be ready for this tournament".
They can now dream of going one better than their third-place finish in 1998, which marked their first participation in the World Cup finals as an independent nation. Come full-time it was Messi leading the celebrations.
Messi: Look (shows his ankle).
Mascherano, his unexplained black-eye having now disappeared, later posted a picture of his lakeside view at the team's training base on Instagram, highlighting that he was in "peace".
They claim that Sampaoli was merely "informing him of the change".
"It's all great for the history books in Croatia but if we don't win against Denmark, when someone asks you what you did, what can you say?"