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Argentina held in Peru
Argentina remain top of the South American World Cup qualification group despite being held to a 1-1 draw against Peru in Lima.
Rondon struck in either half as Venezuela moved into sixth in the table on 11 points, just one below Chile, who occupy the last automatic qualifying position at the moment.
Salomon Rondon's double gave Venezuela a shock 2-0 victory at Paraguay.
Referee Carlos Amarilla refused to award a penalty and Ecuador then saw Manchester United midfielder Antonio Valencia sent off in injury-time.
However, the hosts were a perhaps a touch fortunate after keeper Fernando Muslera appeared to foul Cristian Benitez in the area.
Former Manchester City striker Felipe Caicedo put Ecuador ahead with a seventh minute penalty before Edinson Cavani gave Uruguay a share of the spoils in the 66th minute.
Colombia are now on 13 points in the CONMEBOL qualifying zone, the same as Ecuador, who played out a 1-1 draw with Uruguay in Montevideo.
"This is a magnificent win for us. We were sure it was going to happen," Falcao said. "This is the result of the maturity of a team who did not give up after Chile's goal.''
Two minutes later, Teofilo Gutierrez linked up with Falcao before finishing with aplomb although Colombia were also then reduced to 10 men when defender Abel Aguilar was sent off for a second bookable offence with six minutes remaining.
However, James Rodriguez levelled just before the hour mark with a free-kick, while Aldo Ramirez teed up Falcao, who put Colombia ahead in the 73rd minute at the Estadio Monumental.
In the 41st minute, the Colombian players stopped running as they expected referee Victor Carrillo to blow a foul on Edwin Valencia. They left Matias Fernandez unmarked and the Chilean forward's strike from outside the box beat Colombia keeper David Ospina.
Despite midfielder Gary Medel being sent off in the 34th minute for hitting Luis Perea, Chile took a half-time lead through Matias Fernandez following a blunder from the Colombian defence.
In an encounter that saw both sides reduced to 10 men, Atletico Madrid striker Falcao scored one and set up another as Colombia remained in second place in the table.
Radamel Falcao put in a man of the match display as Colombia came from a goal down to claim a surprise 3-1 win at Chile.
Argentina equalised just before the half-time interval with their first genuine chance in the 38th minute. Higuain finished Ezequiel Lavezzi's cross to notch his sixth goal of the qualification campaign.
But it was not long before Peru took the lead as defender Carlos Zambrano slotted home Farfan's low cross from the right in the 19th minute.
Argentina could have conceded in just the third minute when Peru were award a penalty after Angel Di Maria fouled Jefferson Farfan in the box. However, Sergio Romero saved Claudio Pizarro's spot kick.
Carlos Zambrano had put the hosts in front after 22 minutes but Real Madrid striker Gonzalo Higuain drew level for Argentina at the Estadio Nacional.