Gonzalo Higuain and Angel Di Maria capitalised on excellent attacking play in the first-half to put the South Americans ahead, before an own goal by the Super Eagles extinguished hopes revived momentarily by Chinedu Obasi's strike.
The teams kicked off in front of a Bangladeshi crowd heavily weighted in favour of the Argentines, and in particular Lionel Messi. The Albiceleste quickly put themselves on the front foot, enjoying the lion's share of possession against a Nigeria side looking to pressure in their own half and hit on the counter.
The first chance of the match fell to Jose Sosa, who saw his half-chance smothered by Aiyenugba after Angel Di Maria did well to rob the ball in Nigeria territory. The Super Eagles also had opportunities, with Victor Obinna trying his luck from the edge of the area only to blast high and wide.
There were few chances in the first 45, but Argentina took them with class. The scoreline was opened with 24 minutes on the clock, Gonzalo Higuain latching on to a perfect pass by Messi to blast past the keeper and put Argentina in the ascendancy.
Nigeria barely had time to return the ball to the centre circle before the advantage was doubled. Messi was once more at the heart of the action, as he carved open the defence with a spectacular slaloming run. Aiyenugba denied the Barcelona star, but Angel Di Maria was on hand to poke in the rebound for a goal that without doubt belonged to the inspired 'Pulga'.
The half came to an end with Argentina searching for a third, and they nearly found it thanks again to their No. 10. Messi once more surged forward and released a stinging shot, but was thwarted by the keeper to ensure that both teams went in with the scoreline reading 2-0.
The second period had barely begun when Nigeria gave themselves a fighting chance. Defensive hesitance from Argentina allowed John Obi Mikel the ball, and he cut back well to tee up Chinedu Obasi for the Africans' first. Ahmed Musa then fired just wide of the post, as the Super Eagles strived to put themselves back in the game.
Just when it looked like Nigeria were back in to the game, however, Higuain was on the hand to restore the difference. The Real Madrid man picked up a neat pass from Di Maria and, after his first effort was saved, he forced Uwa Elderson to turn the ball into his own net. The goal did not discourage Samson Siasia's team though, and they continued to push forward against an Argentina team looking far more withdrawn from the first half.
Both teams made several changes as the game drew to a close, and Sergio Aguero went close to killing the game off when his effort was deflected behind. Chibuzor Obonkwo was then extremely lucky to stay on the field, booked for a vicious two-footed tackle on Jose Sosa which should have earned a straight red. The scoreline refused to budge, however, and both teams were happy to play out the remaining minutes and settle for a 3-1 triumph in favour of the South Americans.
Coach Alejandro Sabella will be content with the win over a feisty opponent, although there will be some concerns over the loss of rhythm in the second half. Nigeria, meanwhile, can take heart from how they rallied from a dire situation, making life difficult for the Albiceleste when lesser sides would have crumbled.