A draw in Montevideo would have earned the Cafeteros a place in next summer's finals in Brazil, but late goals from Edinson Cavani and Christian Stuani gave Uruguay the victory.
The result boosted Uruguay's hopes of qualifying as it kept them in fifth place - the position that will face a play-off against Jordan for a World Cup finals spot.
Colombia dominated in the opening stages at the Estadio Centenario but Uruguay snatched victory through Cavani's 76th-minute header and a Stuani strike four minutes later.
"In the second half, our attitude was very different," Uruguay and Liverpool striker Luis Suarez told reporters in Montevideo.
"We played much better than in the first half. We built more opportunities to score and you can see it in the score."
Colombia's Argentina-born boss Jose Nestor Pekerman struggled to hide his disappointment, saying: "Our idea was to qualify (to the World Cup) tonight.
"We were determined to do so, but we couldn't. I think a lot of what Colombia has was shown tonight. We tried to play good football against very important rivals."
Uruguay moved level on points with fourth-spotted Ecuador - but behind on goal difference - thanks to bottom-placed Bolivia holding the Ecuadorians to a 1-1 draw in La Paz.
The hosts dominated a goalless first half before taking the lead two minutes into the second period through substitute Jaime Arrascaita.
Felipe Caicedo got the visitors back on level terms from the penalty spot 10 minutes later after Ronald Raldes had fouled Jefferson Montero in the box.
Sixth-placed Venezuela remained three points behind Uruguay courtesy of a 3-2 win against Peru in Puerto la Cruz.
Paolo Hurtado put the visitors ahead in the 19th minute, only for Salomon Rondon to restore parity nine minutes before the interval.
Cesar Gonzalez's penalty edged the Vinotinto ahead just after the hour mark and Romulo Otero stretched their advantage in the 76th minute.
Carlos Zambrano gave Peru a glimmer of hope by reducing the deficit three minutes from time, but they could not find an equaliser.