Napoli striker Gonzalo Higuain rifled home the only goal for Argentina as the tournament favorites downed the Reggae Boyz in Vina del Mar to clinch top spot in Group B ahead of Paraguay and Uruguay.
But it was another patchy performance from the 2014 World Cup quarter-finalists, who struggled to break down a team ranked 62 places below them in the latest FIFA standings.
Argentina coach Gerardo Martino blamed weariness for his side's disjointed performance, and said his side were looking forward to some rest in the six-day break before next Friday's quarter-final.
"At the end though it was a bit tedious but we did what was necessary. Physically we struggled a bit in the second half."
Argentina will play either Ecuador or the third placed team from Group C in the last eight.
- 'Tough schedule' -
====================
"There are things to fix," Martino said. "We've got six days' rest now before the quarter-finals and I think we need them.
"We've had three matches in a week so it's been a tough schedule."
At the final whistle, striker Deshorn Brown posed for a selfie with Argentina skipper Messi, who was unable to mark his century of caps with a goal.
The Barcelona superstar meanwhile was happy to swap the jersey from his 100th international appearance with Jamaican midfielder Jobi McAnuff, who plays in the fourth tier of the English football league system.
Jamaica captain Rodolph Austin said he was proud of his team's performances in Chile, as they headed home from the tournament after three consecutive 1-0 defeats in the first round.
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