An impressive attacking display from Messi, Gonzalo Higuain and Angel Di Maria saw off Paraguay in Cordoba.
Real Madrid winger Di Maria got Alejandro Sabella's side off to the perfect start with the opening goal after just two minutes.
Jonathan Fabbro equalised from the penalty spot 14 minutes later but Higuain restored the hosts' lead soon after the half-hour mark and Messi's second-half free-kick put the result beyond doubt.
Argentina headed into the game on a five-match winning streak and raced out of the blocks, Di Maria's precise left-footed finish rounding off good work from Ezequiel Lavezzi on the right before the visitors had settled.
Paraguay looked for a swift response, but defender Antolin Alcaraz sent his header from Victor Ayala's corner narrowly wide.
They were level soon after, though, when Estudiantes midfielder Rodrigo Brana inexplicably handled the ball inside the box, and Argentina-born Fabbro made no mistake from the spot.
Argentina appeared nervous after being pegged back, but they were soon back in front as Higuain capitalised on a defensive mistake on the edge of the area to pick his spot at the far post.
Messi almost stretched the advantage immediately with a free-kick but saw his effort hit Justo Villar's right post.
The Barcelona forward was again denied by the woodwork at the start of the second half after mesmerising two defenders and beating Villar.
It was third time lucky for Messi, though, when his 64th-minute free-kick went in via the left upright to seal Argentina's win.
Paraguay coach Gerardo Pelusso attempted to get the visitors back in the game by introducing Benfica's Oscar Cardozo and Malaga's Nelson Haedo Valdez.
But they failed to trouble the Argentina defence, with the best chance of a further goal coming at the other end when Higuain was through one on one but Villar got the better of the duel.
"It was an special night because we wanted to give a victory to these people and, thanks God, we did it," said Messi, who was given a huge ovation by the crowd at the Estadio Mario Alberto Kempes at the final whistle.
"The posts gave me extra work but then I managed to score with the free-kick. It was a good night also because we overcame a difficult moment, when Paraguay levelled the game."
He added: "It's not so important to be leaders. The main target is to qualify for the World Cup and we're on the right path."
Di Maria said: "It's very nice to play outside Buenos Aires. Today [Friday] the fans packed the stadium and we put on a good show.
"I think we were clearly superior. Besides our attacking power, they hardly created any danger for our defence.
"We are on a good streak and we want to keep it going for as long as possible."
The win handed Sabella's team sole possession of top spot in the South American zone on 13 points - one clear of Chile and Ecuador.
Higuain said: "We already had our off round and, despite that, we are at the top. If we maintain our level, the dream of being in Brazil 2014 will be very close."
Paraguay, meanwhile, were second-bottom having collected only four points from six games.
Argentina face Peru in Lima on Tuesday, while Paraguay tackle Venezuela in Asuncion.