It was Argentina's first win in four qualifiers without injured captain Lionel Messi and leaves them with five points, still seven behind leaders Ecuador who beat Venezuela 3-1 away.
Surprise package Ecuador extended to 12 points their perfect start, which began with a 2-0 upset victory over Argentina in Buenos Aires last month.
Colombia, who began with a 2-0 home win over Peru, have four points following their 1-1 draw in Chile last week.
Biglia began an attack in the Argentina half, Ever Banega carried on the move with a pass out to Ezequiel Lavezzi on the right and his low cross beat David Ospina, allowing Biglia, following up, to tap into the unguarded net.
Argentina, also without forward Sergio Aguero, had chances to make the result safer but substitute striker Paulo Dybala had a goal disallowed and minutes later hit the post.
They had to overcome the heat and humidity and a noisy 45,000 crowd for a second successive victory in Barranquilla.
The Caribbean port city was where Argentina got their previous World Cup qualifying campaign off the ground with a 2-1 win in November 2011 on the way to last year’s final in Brazil.
Argentina wrested control from Colombia after withstanding early pressure and could have scored in the 12th minute but Gonzalo Higuain shot over from Angel Di Maria’s cross.
They survived a scare when goalkeeper Sergio Romero misjudged a backward header from central defender Rogelio Funes Mori and had to make a diving save.
Angel Di Maria had a chance just before the interval when he had only Colombia keeper David Ospina to beat but his shot skimmed the outside of the post.
Argentina’s midfield of Biglia, Banega and Javier Mascherano ensured the visitors had more territorial control in a tight second half, moving well to deny Colombia space to build moves.
“We knew it wouldn’t be an easy match... Argentina occupied space well and created room for themselves to counter-attack while denying us room to get closer to their goalkeeper,” substitute striker Luis Muriel told reporters.
Muriel played a key role in Thursday’s 1-1 draw in Santiago in a performance Colombia were unable to repeat in Barranquilla.
The top four at the end of the 10-team, 18-match South American group in two years' time will qualify for the 2018 Russia finals with the fifth-placed team going into an intercontinental playoff.
(Reporting by Jose Miguel Gomez; Writing by Rex Gowar; Editing by Steve Tongue and Ken Ferris)
