Argentina weathered an early storm at the Estadio Nacional before Messi broke into the box, sidestepped a defender and beat goalkeeper Miguel Pinto in the 28th minute.
Three minutes later Higuain came into the box, rounded two defenders and curled a left-foot shot into Pinto's far corner.
Felipe Gutierrez pulled a goal back for the home side in added time.
Argentina are three points ahead of second-placed Ecuador with 20 points from nine matches, with Messi and Higuain joint top scorers with Uruguay's Luis Suarez on seven.
"We faced a team who always create problems for whatever side team they come up against. In the first half, there were more chances for both sides," Argentina coach Alejandro Sabella told reporters.
Argentina had to weather an early storm, with Chile forward Sebastian Pinto missing two chances in five minutes.
Alexis Sanchez and Mauricio Isla, who played together at Udinese, combined well to cause Pablo Zabaleta problems at left back, and Mark Gonzalez missed another chance for Chile in the 15th minute when his header was deflected away by goalkeeper Sergio Romero.
Argentina threatened for the first time in the 18th minute when Higuain stole the ball from Gonzalo Jara and his shot was saved by Pinto.
Ten minutes later, Messi received a long pass from midfielder Fernando Gago, evaded a defender and put Argentina 1-0 up with his first shot on goal.
Three minutes later, Higuain took a cross-field pass from Angel Di Maria, eluded two defenders and doubled the visitors' lead with a class finish.
Striker Sergio Aguero shook the Chile post in the 44th minute after another Jara mistake and a few seconds later Higuain missed with a fierce shot.
Chile goalkeeper Pinto kept the score at 2-0 by stopping a delightful lob from Di Maria on the stroke of half-time.
The home side started the second half brightly but were again wasteful in front of goal, forward Pinto squandering a chance in the 54th minute and seconds later he was replaced by Eduardo Vargas.
Pinto came to Chile's rescue in the 68th minute, saving a Messi shot after Argentina broke quickly, but the home side could not take their chances at the other end with midfielder Matias Fernandez and Vargas missing late on.
Chile finally found the net in stoppage time but it was too late to change the outcome of the match.