In a niggly and fractious match, five-time Ballon d’Or winner Messi and Chile captain Gary Medel were given their marching orders eight minutes from half-time after tangling on the goalline.
Sergio Aguero and Paulo Dybala scored the first half goals that ensured victory for Argentina.
But the match will be most remembered for the double sending-off and the melee it sparked.
In what seemed an innocuous clash, a frustrated Messi shoved Medel in the back as the center-back shepherded the ball out of play.
A furious Medel responded by chest-bumping Messi twice in an incident that probably merited no more than a a single yellow card for the Chilean.
Incredibly, Paraguayan referee Mario Diaz de Vivar showed the two captains the red card.
Medel in particular reacted even more angrily as players from both sides squared up to each other and the referee, who lost complete control of the situation.
It took fully five minutes to calm the situation and get Messi and Medel to leave the field.
At this point, already 2-0 down, Chile were in danger of losing their heads and Erick Pulgar was lucky to receive only a yellow card for a stamp on Leandro Paredes that looked a far worse offence that either Messi’s or Medel’s.
Messi had created the opening goal with a quickly-taken free-kick on 12 minutes, picking out Aguero’s clever diagonal run before the forward rounded goalkeeper Gabriel Arias and passed the ball cooly into the empty goal.
Ten minutes later, Dybala doubled the lead with a cool, dinked finish past the advancing Arias after taking a sumptuous Giovani Lo Celso through ball in his stride.
By tha time, Chile had seen influential Manchester United forward Alexis Sanchez limp off with a hamstring injury.
Chile were handed a lifeline when Lo Celso was adjudged to have brought down Charles Aranguiz on the edge of the penalty area, with Arturo Vidal slamming home the penalty on 59 minutes.
Aguero came closest to scoring again but his chipped finish hit Arias in the head.
