The battle for the World Cup's golden boot heated up between Barcelona teammates as Messi latched onto a rebound in just the third minute and then curled in a freekick shortly before halftime to match Neymar's tally of four in three games for Brazil.
One player who may not be in the reckoning for tournament top scorer is Luis Suarez, who is the focus of a FIFA disciplinary investigation after he appeared to bite the left shoulder of Italy defender Giorgio Chiellini on Tuesday and could be facing a lengthy ban.
The 22-year-old Neymar is relishing playing the World Cup at home and thriving on the pressure that brings.
"I'm doing what I've always wanted to do since I was a little kid," he said. "Today my dream is coming true, I'm playing the matches that I've always wanted to be playing."
Karim Benzema and Enner Valencia already have three goals each and will look to score more when France and Ecuador meet in Wednesday's final match. Honduras was facing Switzerland in the day's other Group E match, with both teams still having a mathematical chance of qualifying for the round of 16.
Ahmed Musa matched Messi goal for goal in Porto Alegre, equalizing just a minute after Messi opened the scoring in the third minute and levelling again in the second half after Messi's perfectly curled free kick shortly before the break had put Argentina ahead again. Marcos Roja finally sealed Argentina's win in the 50th.
In Salvador, Edin Dzeko, Miralem Pjanic and Avdija Vrsajevic got Bosnia's goals for its first ever World Cup win and Reza Ghoochannejhad scored for Iran, which had to win and hope Nigeria lost to progress.
While the World Cup goal glut continued on the pitch, Suarez was again hogging headlines with his latest alleged biting incident.
If FIFA rules that Suarez sank his teeth into Chiellini's shoulder, it could suspend him for up to 24 matches or sideline him for a maximum of two two years. The Uruguay and Liverpool star is a repeat offender — he has twice been sanctioned for biting in his turbulent past, first in the Dutch league in 2010 when playing for Ajax and again in 2013 while in a Liverpool shirt. He also has been banned for racially abusing an opponent in England.
Suarez and the Uruguay football federation had until 5 p.m. local time (4 p.m. EDT/2000 GMT) to present FIFA with a documented case for the defence.
Meanwhile, tragedy struck in Nigeria before the country's clash with Argentina, as an explosion killed at least 21 people in a shopping mall in the capital, Abuja. Many shops at the mall have TV screens but it was unclear if the explosion was timed to coincide with the match, which started an hour later.