Paolo Guerrero claimed his second goal of the tournament to give the Peruvians a deserved victory against an under-strength Mexico, stroking the ball home from close range in the 82nd minute after being left unmarked at the far post.
The win put Peru on four points alongside Chile and leaves World Cup semi-finalists Uruguay third in the group on two points, needing a positive result in their final game next week to advance to the quarter-finals.
Having drawn their opener against Peru, Uruguay went in search of a win against Chile and Luis Suarez should have put them ahead after 19 minutes but blasted over after Edinson Cavani had put him through.
Eight minutes later, a mix-up in the Chilean defence left Diego Forlan with a free header from the edge of the six-yard box with Chilean keeper Claudio Bravo stranded, but defender Pablo Contreras cleared the goal-bound effort off the line.
Chile's closest first-half effort came from a bizarre deflection.
Uruguayan defender Diego Lugano attempted to boot the ball clear but it hit Chile's Mauricio Isla and floated over Fernando Muslera towards the Uruguayan goal but came back off the crossbar.
However, nine minutes after the break, Alvaro Pereira broke the deadlock for Uruguay. Suarez was the provider, crossing from the left for the Porto player to stroke home.
Chile went on the attack and in the 65th minute, Jean Beausejour escaped down the left and cut the ball back for Sanchez, who buried a low shot in the far corner of the Uruguayan net to earn his side a point.
"I'm happy with the way the team played," Chile's Argentine coach Claudio Borghi told reporters.
"Let's not forget we were playing against the team that finished fourth at the World Cup and that they had almost the same team as then, and that we were losing, so coming from behind was important."
Six of the opening 10 matches in South America's most prestigious international tournament have ended in draws and invitee Costa Rica, supposedly the weakest team in the competition, are the only side to have won by two clear goals.
The top two teams from the three groups advance to the quarter-finals along with the best two third-place finishers.
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