Messi beat Claudio Bravo from the spot in the 16th minute after Angel Di Maria had been pushed from behind in the first quarter of a poor, tense match on a terrible River Plate pitch.
Argentina, a shadow of the team that finished World Cup runners-up in 2014, moved into third place in the 10-nation South American group on 22 points, eight behind leaders Brazil and one in arrears to second-placed Uruguay.
Brazil earlier beat Uruguay 4-1.
Colombia, who beat Bolivia 1-0 at home, are now in the fourth qualifying place with 21 points, one ahead of Ecuador, who lost 2-1 away to Paraguay and sit in the playoff berth.
"We suffered because we lost the ball but at least we won," relieved Argentina coach Edgardo Bauza told reporters.
Chile, missing suspended midfielder Arturo Vidal but worthy of at least a draw, gave Argentina and early scare when they had the ball in net after a free kick from the left only for Jose Fuenzalida to be ruled offside.
Argentina took the lead when Brazilian referee Sandro Ricci ruled that Fuenzalida had pushed Di Maria as he chased a fine through ball from Javier Mascherano.
Messi sent Bravo the wrong way and buried the ball in the back of the net to a roar from a wildly passionate 60,000 crowd at El Monumental.
Stringing moves together was difficult for both teams on a patchy pitch and Argentina were relieved when the final whistle went after withstanding intense pressure from the Copa America holders, who are now sixth in the group on goal difference.
Argentina central defender Nicolas Otamendi should have scored from a Messi free kick before halftime but blasted a chance over the bar.
Messi was mostly kept quiet by the Chile defence but he had another chance to score from Marcos Rojo's cross from the left only to see his effort go over the bar.
Midway through the second half, Chile's Alexis Sanchez hit the bar with a free kick and goalkeeper Sergio Romero had to get down sharply to prevent a subsequent cross from reaching substitute Nicolas Castillo.
On a disappointing night in front of goal for Chile, Sanchez lobbed a free kick from a similar position high over the bar and Castillo slipped through the defence to meet a cross but steered his shot wide of the near post.
(Editing by Nick Mulvenney)
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