It was a fifth win in six games for Argentina, which now has 20 points and is 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 after 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 past two matches, adding: "We wanted the six points from these matches because we thought we could made a very important step (towards the World Cup).
"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."
Defender Federico Fernandez added: "It was a great game by Argentina. We knew Chile were in need of results but we took a very important result."
Carlos Saucedo scored a hat-trick as Bolivia claimed a surprise 4-1 home win against Uruguay and left the visitor in a difficult position in the World Cup qualifying zone.
Saucedo opened the scoring in the sixth minute and Gualberto Mojica doubled the lead from a free-kick 20 minutes later.
Uruguay coach Oscar Tabarez made two substitutions in the first half by fielding Edinson Cavani and Nicolas Lodeiro for Maximiliano Pereira and Walter Gargano, but they failed to have the desired effect.
Saucedo made it 3-0 shortly after the interval and completed his hat-trick soon after.
Luis Suarez scored Uruguay's consolation 10 minutes from time.
Bolivia claimed only their second victory on the road to Brazil 2014, while fifth-placed Uruguay would be playing a knockout tie with a CONCACAF team if the tournament finished today.
Bolivia coach Xavier Azkargorta is hopeful of making it to the World Cup, adding: "There are 21 points left. We must play the games.
"We'll keep fighting to be as high as possible in the standings. We don't lose faith."
Tabarez was unable to hide disappointment, adding: "Our form is not good. We must keep focused. There are seven finals remaining. Bolivia won deservedly."
Ecuador remains second in the standings thanks to a 1-1 draw in Venezuela.
Juan Arango put the host ahead with a long-distance shot in the fifth minute but Segundo Castillo equalised midway through the half.
In Asuncion, Paraguay finally celebrated a victory after five defeats in a row, as it beat Peru 1-0 thanks to a 53rd-minute header from Pablo Aguilar.