For 82 minutes, the Manchester United striker's national side were on course for a quarter-final meeting with Peru - one of the qualifying third-placed teams - but when Edison Cavani brilliantly headed home from substitute Jonathan Rodriguez's cross, it gave the Uruguayans top spot in Group C and the supposedly easier last-eight tie.
Meanwhile, Chile must face Group B winners Colombia, who finished five points clear of Argentina after winning their first three games.
Alexis overcame the ankle sprain he sustained before grabbing the winner against Ecuador and he played another full 90 at the Maracanda Stadium in Rio de Janiero; the only minutes he has missed so far were the final few against Japan, when he was rested after notching one goal and assisting another in the 4-0 victory.