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.
Two minutes later, Teofilo Gutierrez linked up with Falcao before finishing with aplomb although Colombia were also then reduced to ten men when defender Abel Aguilar was sent off for a second bookable offence with six minutes remaining.
Former Manchester City striker Felipe Caicedo put Ecuador ahead with a seventh minute penalty before Edinson Cavani gave the Uruguayans a share of the spoils in the 66th minute.
Ecuador then saw Manchester United midfielder Antonio Valencia sent off in injury time.
Argentina remain top of the group despite a 1-1 draw at Peru in Lima. Carlos Zambrano had put the hosts in front after 22 minutes but Real Madrid striker Gonzalo Higuain (38) drew level for Argentina.
Salomon Rondon's double gave Venezuela a shock 2-0 victory at Paraguay. Rondon struck in either half as Venezuela strengthened their hold on sixth on 11 points, just one point off an automatic qualifying position.