Higuain put Argentina ahead from Angel di Maria's pass in a counter-attack after seven minutes at the Monumental stadium in Buenos Aires and Messi, whose last goal in a competitive international was against Venezuela in March 2009, netted the second in the 25th.
Higuain chipped in a Di Maria cross from the left seven minutes into the second half and completed his hat-trick when Messi capitalised on a faulty clearance by keeper Claudio Bravo and found the striker with a low pass.
Chile, who beat Argentina for the first time when the teams last met, a 2010 World Cup qualifier in Santiago in October 2008, pulled a goal back through Matias Fernandez on the hour.
Argentina easily outpaced Chile's vulnerable defence and it took Higuain seven minutes to net a through ball from his Real Madrid team-mate Di Maria.
"It's a great joy to start the qualifiers this way, this new era with a new coach," a cheerful Higuain told reporters referring to Alejandro Sabella, who took charge in August after Argentina's disappointing showing at the Copa America as hosts.
Higuain later assisted captain Messi, who scored in the 25th minute right after missing another chance.
The goal was a timely riposte to criticism from some home fans who felt aggrieved at Messi's failure to emulate his lofty standards at club-level for Barcelona with the national team.
As the playmaker marched towards the flag in the 32nd minute to take a corner kick, he received a standing ovation from the crowd in the adjacent terraces.
"It's important for Messi to be able to reverse this collective psychosis," said Sabella. "But it's not the most important thing, for if Messi doesn't score, he creates the situations from where goals are scored."
Messi, appointed captain by Sabella on a tour of Asia last month, said: "The team left a good impression and that's what's important. The squad comes before individual happiness."
As half-time approached, Argentina slowed down and Chile, though limited in attack without injured forward Alexis Sanchez, tried to come back into the game from set-pieces and a long shot from striker Humberto Suazo went just wide.
The interval was enough for the home team to regain the momentum and Higuain chipped in a Di Maria cross from the left seven minutes into the second half.
Eight minutes later, Chile, coached by Argentine 1986 World Cup winner Claudio Borghi, narrowed the gap through Fernandez.
But Messi capitalised on a faulty clearance by Bravo and slid the ball through to Higuain to round off the scoring with half-an-hour left to play.
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