Argentina beat Paraguay 3-1 on Friday to climb to the top of the standings in the South American qualifiers for the Brazil 2014 World Cup.
While Colombia thrashed Uruguay 4-0, Ecuador beat Bolivia 1-0 and Peru defeated Venezuela 2-1.
Argentina now top the standings, with 13 points in six games, ahead of Chile - who were not playing Friday - and Ecuador who have 12. Uruguay have 11 and Colombia are on 10, while Venezuela remain on eight but have played an extra match.
The South American qualifiers grant four World Cup berths directly plus the chance to earn a fifth in a play-off.
Goalscorer Lionel Messi said Argentina were happy with their performance.
"It doesn't matter if we're top. The important thing is to qualify for the World Cup," said Argentine superstar Lionel Messi. "But if we're first, all the better."
Coach Alejandro Sabella was pleased too, but he described his optimism as "moderate, considering the winding path ahead.
"We have to keep our feet on the ground.
Di Maria opened the scoring in the central Argentine city of Cordoba in the third minute, with a shot that deflected off the back of teammate Ezequiel Lavezzi.
In the 17th minute, Paraguay striker Jonathan Fabbro tied the score from the penalty spot.
Gonzalo Higuain again put the hosts ahead in the 30th minute, and captain Messi, who had previously hit the woodwork twice, scored the definitive 3-1 in the 63rd minute.
In Barranquilla in-form Atletico Madrid forward Radamel Falcao put Colombia ahead after two minutes. Teofilo Gutierrez scored a brace in the 47th and 54th minutes, while Camilo Zuniga found the net in injury time.
"We were practical," Gutierrez said.
"With the national team we're a family, and we enjoy this as such."
Colombia's Argentine coach Jose Pekerman looked to the future.
"Let's hope we can play every game like this. If we keep up this level we would get closer to the World Cup," said Pekerman.
In Quito, Ecuador's Felipe Caicedo, scored the only goal of the match from the penalty spot in the 71st minute. As Bolivian players complained that there had been no foul against Luis Saritama.
Peru restored some hope of qualifying for the World Cup with their 2-1 comeback win over Venezuela in Lima. Venezuela veteran Juan Arango put the visitors ahead in the 42nd minute, but Jefferson Farfan sealed his team's recovery with a brace, in the 47th and 54th minutes.
The result allowed Peru to leave the bottom of the standings and climb to seventh place, with six points. Bolivia - who have played seven qualifying rounds so far - and Paraguay trail with just four points.
The South American World Cup qualifiers are set to continue Tuesday with the following fixtures: Chile-Colombia, Uruguay-Ecuador, Paraguay-Venezuela and Peru-Argentina.
Brazil are directly qualified as hosts for the 2014 finals and don't have to play in the South American qualifiers. On Friday, they struggled but eventually managed to beat South Africa 1-0 in friendly in Sao Paulo.