Falcao's brace saw Colombia win 2-0 at home to Paraguay in World Cup qualifying, while Lionel Messi scored twice as Argentina beat Uruguay 3-0.
Atletico Madrid star Falcao's goals helped Colombia keep up their pursuit of Argentina at the top of the South American World Cup qualifying table.
After a goalless first half in Barranquilla, Falcao scored in the 52nd and 88th minutes to seal their third consecutive qualifying win.
"Paraguay were a very tough obstacle to break down," Falcao said. "We had to really fight hard to get the job done.
"Our main target is the World Cup. We are on the right path but we have a lot of work to do."
Jose Nestor Pekerman's team have now 16 points, one less than Argentina, who beat Uruguay 3-0 with a brace from Lionel Messi and a goal from Sergio Aguero.
For rock-bottom Paraguay, it was their sixth defeat in eight games.
"Colombia were fair winners," said Paraguay coach Gerardo Pelusso. "We mustn't continue thinking about the defeat. If we want to have any chance of qualifying we must react immediately."
Alongside Colombia on 16 points are Ecuador, who came from behind to beat Chile 3-1 at home.
The star of the game was Lokomotiv Moscow's Felipe Caicedo, who scored in the 32nd and 55th minutes, while Segundo Castillo completed the scoring for the hosts in the injury time.
It had not looked so easy in Quito when Juan Paredes Reascos sent the ball into his own goal in the 24th minute, but Chile could not maintain their rhythm and had Pablo Contreras and Juventus' Arturo Vidal sent off.
"We have a crucial chat with the players at half-time, when we were losing. They corrected all the mistakes they made," Ecuador's coach Reinaldo Rueda said.
"This group of players are very focused on reaching the World Cup, they want to make history in Ecuadorian football."
With this defeat Chile are level with Uruguay in the fifth position, both with 12 points.
Finally, in La Paz, Bolivia and Peru drew 1-1, Juan Carlos Marino putting the visitors ahead in the first half and Alejandro Chumacero levelling shortly after the break.
