The attacker went level at the top of the Golden Boot standings, helping to prevent Ahmed Musa's doubles from gifting Stephen Keshi's men a point
Barcelona superstar Messi was at his brilliant best at Estadio Beira-Rio on Wednesday, following up a stunning half-volley with a superb free kick.
His efforts, though, were twice cancelled out by the equally impressive Ahmed Musa as Nigeria put in a spirited display.
They eventually succumbed as Marcos Rojo's unorthodox finish five minutes after half-time ensured Argentina went through with a maximum haul of nine points.
While Nigeria entered their final Group F fixture needing a draw to guarantee their progression, Bosnia-Herzegovina's 3-1 triumph over Iran meant that they qualified anyway.
The Africa Cup of Nations champions look likely to face France in the last 16, with Argentina probably on course to tackle Switzerland or Ecuador - with Group E set to be concluded later on Wednesday.
Any hopes Nigeria had of getting the point they required were dented immediately as Messi fired the two-time champions ahead.
Angel Di Maria was instrumental, charging into the area before unleashing a fierce strike that hit the post, struck the back of goalkeeper Vincent Enyeama and bounced back onto the woodwork.
Unfortunately for the African side, as the ball ricocheted back into the area, Messi was on hand to power home a sublime half-volley.
But Nigeria were not willing to be the supporting act for too long and levelled a minute later, Musa picking up the ball on the left flank before cutting inside and expertly bending a curling effort beyond Sergio Romero.
Argentina required a response, and they almost found one soon afterwards when Gonzalo Higuain poked a shot wide after getting on the end of Messi's through-ball.
It was Di Maria who was causing the greatest threat, his low 25-yard strike forcing a good save from Enyeama. Yet Messi assumed centre stage again to re-establish his side's lead.
Having forced a fine save from Enyeama with a curling set-piece, he left the Nigeria goalkeeper stranded from exactly the same position in first-half injury time after the mercurial Barcelona man had been brought down by Kenneth Omeruo.
Far from downhearted, Nigeria found an almost immediate riposte after the interval as Musa ran into a huge gap between the Argentina centre-backs and slotted past Romero, having been picked out by Emmanuel Emenike.
However, as the momentum swung once more, Argentina moved in front for the third time just three minutes later, Rojo kneeing Ezequiel Lavezzi's corner home in unorthodox fashion.
Suddenly attacking with renewed verve, Alejandro Sabella's men began to look increasingly threatening - with Enyeama having to be on high alert to keep out a Higuain effort before Messi slid a shot wide.
The Argentina captain was withdrawn in the 63rd minute, to a rapturous ovation from the crowd.
Sabella's side barely missed a beat in his absence, although some poor finishing - summed up by Di Maria hitting straight at the goalkeeper towards the end - ultimately meant that they did not add to their tally.