Leandro Damiao scored the only goal of the game in the 11th minute and helped Dorival Junior's side, who won the title in 2006 and 2010, claim a narrow lead.
Damiao finished off great play by Argentinian playmaker Andres D'Alessandro to beat Once Caldas goalkeeper Luis Enrique Martinez.
The return leg is next Wednesday in Manizales with the winner to progress to Group One alongside Santos, Juan Aurich of Peru and Bolivia's The Strongest.
Inter defender Indio told Globo TV: "The team gave no opportunities to the rivals to play with the ball, something Once Caldas do very well."
Damiao added: "Winning is important, but nothing is finished."
In Bolivia, another Brazilian team were not as lucky as Flamengo lost 2-1 at Real Potosi.
The Bolivian side came back from a goal down to defeat the Brazilian giants who included former Barcelona and AC Milan playmaker Ronaldinho.
Fine individual play by Leo Moura was finished by Luiz Antonio as Flamengo opened the scoring in the 30th minute.
However, Roly Sejas crossed for Claudio Centurion who headed home the equaliser three minutes later.
Twelve minutes after the interval, another cross - by Rosauro Rivero this time - was headed home by Edgardo Britess for a Real Potosi victory.
The winners will qualify for Group Two where they would meet Emelec of Ecuador, Paraguayan giants Olimpia and Argentina's Lanus.
Real Potosi midfielder Eduardo Ortiz told Fox Sports: "Flamengo are a great team and play very good football, but we never gave up even when a goal down.
"The return match will be hard, very tough and we have to work on a number of aspects."
In Chile, hosts Union Espanola defeated Mexico's Tigres 1-0 with Gonzalo Barriga scoring the winning goal in the 57th minute.
They are fighting for a berth in Group Three alongside Universidad Catolica of Chile, Colombia's Junior and Bolivian side Bolivar and will define the tie next Thursday.
Tomorrow night, five-time champions Penarol meet Venezuela's Caracas in Uruguay in the first leg of the tie that will put one of them in Group Eight along with Universidad de Chile, Argentina's Godoy Cruz and Colombian giants Atletico Nacional.