Messi had been forced to delay his debut in the tournament after a slow recovery from a lower back injury, with Argentina coach Gerardo Martino surprisingly naming him amongst the substitutes once more.
But Messi wasted no time in stamping his genius on the tournament after coming on in the 61st minute to replace Augusto Fernandez with Argentina leading the Group D game 1-0.
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An electrifying cameo from the Barcelona superstar began with his first goal of the tournament on 68 minutes, finishing with aplomb after Gonzalo Higuain's shot bounced off a Panamanian defender into his path.
But there was no question of luck with his second, with Messi curling a wonderful free-kick into the top corner to bring the Soldier Field crowd to its feet in the 78th minute.
With Panama's heads down, Messi then duly completed his quick-fire hat-trick -- skipping clear of a marker inside the penalty area to finish emphatically for 4-0.
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Aguero's Manchester City team-mate Nicolas Otamendi had opened the scoring for Argentina in the seventh minute, heading home an Angel Di Maria free-kick from close range.
The victory sees Argentina, convincing 2-1 winners over Chile in their opening game, guaranteed a spot in the last eight with one group game remaining.
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The only blemish on the evening was an injury to Angel Di Maria, who limped off in the first half to extend his miserable record of injuries in major tournaments.
The Paris Saint-Germain winger was injured in the 2014 World Cup, missing the final, and was also injured during last year's Copa America in Chile.
Argentina are now firmly on course to top Group D, with only one game against pointless Bolivia to come.
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