Strikers Falcao, Alexis Sanchez and Edinson Cavani all scored as Colombia ate into Argentina's lead, Chile notched a second successive win and Uruguay revived their hopes in South American World Cup qualifying on Tuesday.
Falcao's early penalty, taking his tally to seven in the competition, put Colombia on the road to a 2-0 home win over Peru that leaves them three points behind leaders Argentina with a game in hand.
"Falcao was essential in the first half as Peru were unable to deal with his movement. He makes fantastic runs (off the ball)... the 'Tiger' is phenomenal," Colombia coach Jose Pekerman told reporters.
Cavani struck a fine goal as Uruguay beat Venezuela 1-0 away for their first win in seven qualifiers, lifting the 2010 World Cup semi-finalists up to fifth in the nine-nation group, which would earn them a playoff should they maintain the position.
Uruguay leapfrogged Venezuela, a well-drilled outfit looking to take their country to the finals for the first time in Brazil next year, on goal difference with four matches remaining.
"We were aware that it could have all been over for us today," Uruguay coach Oscar Tabarez, deprived of top scorer Luis Suarez through suspension, said.
"We can't say the situation has got comfortable but it's an important step."
Venezuela remain confident of qualifying, despite the setback
"We still have chances and I'm not going to surrender," coach Cesar Farias said.
"We dominated the whole match but it's not about who deserves the win, it's about who scores the goals," captain Juan Arango added.
Chile benefited from the revived goal instincts of Sanchez and the return after eight years of 33-year-old midfielder David Pizarro in a 3-1 home win over Bolivia that consolidated fourth place behind Ecuador on goal difference.
"David gave us a lot of clarity, the possibility of many assists and depth. I'm very pleased with his performance," Chile coach Jorge Sampaoli said.
Ecuador will rue their poor finishing after failing to take more than one goal from an endless string of corners and free kicks in a 1-1 draw with an Argentina side missing Lionel Messi for an hour and struggling in the thin air in Quito.
In two qualifiers this month, Ecuador have picked up only one point and slipped in the standings while Chile, equal on 21 points, are breathing down their necks and Uruguay and Venezuela pose a latent threat.
Ecuador's run of six home victories in as many matches was halted by Argentina, who took an early lead with a Sergio Aguero penalty, and they now have only one fixture at high altitude, Uruguay in October, out of their four remaining qualifiers.
Argentina, who have drawn their last three matches albeit two at high altitude, have a bye in the next round on Sept. 6 when Colombia can catch them at the top if they beat Ecuador at home.
The top four teams at the end of the qualifiers in October will go through to the Brazil finals. The fifth-placed team, at present Uruguay on 16 points, will enter a playoff against an Asian qualifier in November for another spot.