The Colombians, playing at their favourite home ground, the Metropolitano in hot Barranquilla on the Caribbean coast, have 10 points from six matches in the South American group.
Uruguay, who fell to their first defeat in six qualifiers, have 11 points, two behind leaders Argentina and one behind second-placed Chile.
"It was a key match for Colombia, we needed a win like this, the whole team played to a high standard," coach Jose Pekerman said of their first home win in the qualifiers.
"Colombia can beat any rival, today they showed that, but it's not something we can assure, we have to work a lot," added the Argentine, his country's World Cup coach in 2006, who took charge of Colombia after Leonel Alvarez was sacked in November following a 2-1 home defeat to Argentina.
Colombia stunned the Uruguayans by taking the lead after two minutes when Falcao leapt between two defenders to head home Camilo Zuniga's right cross.
Uruguay were on the back foot for long spells and struggled to control Falcao while Gutierrez was caught in the offside trap several times in the first half.
Not so in the second half as, with Uruguay midfielder Alvaro Gonzalez replacing defender Mauricio Victorino at the break, Colombia put the game out of their reach with Gutierrez's goals in the opening seven minutes of the second half.
Gutierrez raced on to a through ball from midfielder James Rodriguez to shoot past goalkeeper Fernando Mulsera in the 47th minute and he added his second five minutes later from close range from Rodriguez's cross.
Muslera prevented a bigger rout with good saves from Rodriguez, Macnelly Torres and Darwin Quintero but was well beaten by defender Zuniga for Colombia's fourth in stoppage time.
