Colombia, who crushed Uruguay 4-0 at home on Friday, joined Argentina at the top of the South American group on 13 points, at least until Lionel Messi's side met Peru in Lima later on Tuesday.
Chile were down to 10 men from the 34th minute when midfielder Gary Medel was sent off for slapping defender Luis Perea, who theatrically fell to the ground, in the face.
The hosts nevertheless took the lead five minutes before the interval with a fine free kick from playmaker Matias Fernandez.
Goalkeeper Claudio Bravo then kept Chile in the match with a string of fine saves although he was helpless with midfielder James Rodriguez's free-kick equaliser just before the hour which went in off his left-hand post.
Colombia's Argentine coach Jose Pekerman, appointed late last year and instrumental in their recovery from a poor start to the qualifiers, made a telling substitution in midfield in the 73rd minute, bringing on Aldo Ramirez for Macnelly Torres.
Ramirez had an immediate impact with a fine through ball to Falcao who steered it past Bravo to put Colombia ahead in the 74th with his third goal in two games.
Gutierrez, who like Falcao had scored twice against Uruguay, increased the visitors' lead three minutes later when he took a pass from his strike partner on the left and beat Bravo with a low shot inside the near post.
Colombia midfielder Abel Aguilar was sent off three minutes from time for handball, his second booking.
"We got three points that take us nearer to what we want. Chile had a very good first half but we were able to come back and we finished very well," Pekerman told Fox Sports.
"This is thanks to my family, my personal trainer and my psychologist so that I could do things properly," said the mercurial Gutierrez, recalled by Pekerman following a troubled spell at Racing Club in Argentina.
"We have a good understanding [with Falcao], this is a very nice family," he added referring to the Colombia squad.
"Pekerman has given us a lot in the tactical aspect and in the mental aspect," Rodriguez said.
