Atletico Junior striker Teofilo Gutierrez was the star of the show for the Cafeteros with two goals, with Atletico Madrid forward Radamel Falcao and Napoli defender Juan Camilo Zuniga also on target.
The win gave Colombia six points from a possible nine since Argentinian coach Jose Nestor Pekerman took charge.
"We have had a few months here, but I think we're on a good path," said Pekerman, who led his country in the 2006 World Cup.
"The team showed that we can defeat anybody. We needed a triumph like this for the fans.
"If we maintain this level, we can seriously fight for a place at Brazil 2014."
A delighted Gutierrez added: "The national team is like a family to me, therefore I'm very happy. I think the result was fair. We played better and were in control against a very difficult team like Uruguay."
In contrast, the Uruguay players were downbeat.
"The only thing we can do to forget this defeat is overcome Ecuador (on Wednesday AEST)", coach Oscar Tabarez said, before praising the opposition.
"They clearly improved their level in recent games and certainly will fight for a World Cup berth."
The result left Uruguay in fourth place - two points behind Argentina, which moved top by beating Paraguay 3-1 in Cordoba through goals from Angel Di Maria, Gonzalo Higuain and Lionel Messi. Jonathan Fabbro was on target from the penalty spot for Paraguay.
Ecuador climbed to joint second place in the standings, alongside Chile on 12 points, after Felipe Caicedo's 70th-minute penalty secured a 1-0 win over Bolivia in Quito.
"Everyone thought we would score a lot of goals, but the truth is that Bolivia were very hard rivals, so this triumph is very valuable," Ecuador coach Reinaldo Rueda said.
Bolivia debutant Xabier Azkargorta was angry with Venezuelan referee Juan Soto over the award of the spot-kick.
"It was a big mistake and it was the decisive factor in the match," he said. "Anyway, now all we can do is work hard to recover."
Peru battled from a goal down to sink Venezuela 2-1 in Lima.
A Juan Arango free-kick just before half-time put the Vinotintos ahead, but a brace from Schalke striker Jefferson Farfan saw Sergio Markarian's side register their second win of the qualifying competition.
The visitors' misery was compounded by a late red card for defender Gabriel Cichero.
The South American qualifying action continues on Wednesday, when Chile faces Colombia, Uruguay plays Ecuador, Paraguay takes on Venezuela and Peru hosts Argentina.