Messi, cheered by fans with his every touch, set up Gonzalo Higuain for the opening goal after 24 minutes and it was from his mesmerising run and shot that Angel Di Maria doubled the lead two minutes later.
Nigeria pulled one back through substitute Chinedu Obasi soon after the restart but an own goal from Elderson midway through the half restored Argentina's two-goal cushion.
"He [Messi] did not score but he assisted in all three goals. He was the best player in the match. It does not matter whether he scores of not," Argentina coach Alejandro Sabela told reporters.
"Nigeria have some very fast strikers so I had to be a bit extra cautious putting an additional defender in the line-up. But our midfield made all the difference with Messi providing some good passes."
Messi entertained the Bangladesh fans right from kick-off and the playmaker went close to breaking the deadlock on 15 minutes when his freekick whistled inches past the post.
A strong Argentina side then went in front thanks to Messi's astute chipped past that found an unmarked Higuain and he fired home.
Argentina's second soon after owed much to a brilliant jinking run by Messi who beat three defenders before seeing his curling shot saved by Dele Aiyegnuba. The keeper was powerless though from stopping Di Maria tapping in the rebound.
Messi almost grabbed a third in first-half stoppage-time but this time was denied by a fine save by Dele.
Nigeria coach Samon Siasia sent on Obasi for the second half and he made an immediate impact by netting from close range after a deflected shot from John Obi Mikel fell to him.
Fellow substitute Ahmed Musa then fired wide but Argentina grabbed a third goal on 65 minutes when Elderson put through his own net.
"It was so obvious that Messi did make the difference," said Siasia.
"We tried our best to stop him but you know he is the world's best player. Whenever he gets the ball he made a problem for us."
