It was a fifth win in six games for Argentina, who have 20 points and are three clear of Ecuador in the standings.
Messi opened the scoring in the 27th minute with his 14th goal in 14 appearances under national team coach Alejandro Sabella.
And Higuain made it 2-0 just three minutes later after collecting a long pass from Angel Di Maria and firing past Miguel Pinto.
Higuain was forced off with an apparent ankle injury in the second half following a bad tackle by Gonzalo Jara, while Chile got on the scoresheet in injury time through Felipe Gutierrez.
Messi was delighted to claim two wins from the last two matches, adding: "We wanted the six points from these matches because we thought we could made a very important step.
"The tournament is very even. There were some results that helped us escape a little bit, but we must keep working.
"There are some friendly games ahead so we should continue training in order to keep gaining points in March, when the qualification resumes."