The five-time Ballon d'Or winner appeared to be the victim of shoving by Chile's Gary Medel, but the referee sent both players off after 37 minutes with Argentina already two goals to the good.
Messi provided the assist for Sergio Aguero's 12th-minute opener before Juventus forward Paulo Dybala doubled Argentina's lead, but the first half ended with protests against the contentious red cards.
There were 21 fouls before the break and sparks continued to fly as Chile were awarded a penalty just before the hour, Arturo Vidal scoring from the spot.
Reinaldo Rueda's men failed to force an equaliser, but there was time for three further bookings that took the tally of cards shown to nine at the end of an explosive encounter.
Aguero lashed a shot narrowly wide after seven minutes but made amends moments later when Messi's nonchalant free-kick picked out the Manchester City striker, who rounded Gabriel Arias before slotting home from a tight angle.
Chile's Alexis Sanchez limped off clutching his hamstring before Arias made a diving save from an 18-yard Messi drive but was beaten again when Dybala controlled Giovani Lo Celso's throughball and chipped over the goalkeeper from the edge of the six-yard box.
Dybala sent a flying volley just wide before a volatile first half turned nasty when Medel pushed Messi around the pitch only for the referee to send both players off amid vociferous complaints on all sides.
The second half began with a a penalty claim, Charles Aranguiz appearing to bundle Aguero over in the box, but the referee saw no foul.
He awarded a penalty to Chile when Lo Celso slid in late on Aranguiz and Vidal lashed the spot-kick straight down the middle.
Lionel Scaloni sent on Angel Di Maria for Dybala and the winger embarked on a mazy dribble past several Chile players before selling Aguero slightly short with his final ball and the striker fired tamely at Arias with the last clear chance of the game.
Follow us on Twitter @AzerNewsAz