The forward, who is in negotiations to join European champions Barcelona from Udinese, scored with an accomplished finish after 64 minutes to cancel out Alvaro Pereira's opener, which came after 53 minutes.
The result leaves Chile top of Group C thanks to a 2-1 win over Mexico in their opening game, but Uruguay, who under Oscar Tabarez reached the semi-finals of the World Cup, have only two points from two games and are in danger of early elimination.
Uruguay were in need of a victory after a disappointing opening draw with Peru and almost enjoyed a superb start. After 19 minutes, Edinson Cavani set Luis Suarez free with a clever flick on the turn but the Liverpool man spurned a glorious chance when rifling a volley that clipped the bar.
Chile, elusive and fluid in an unconventional 3-3-1-3 formation, were causing problems with their movement and intelligent use of the ball, although all too often they resorted to shots from range, with midfielder Arturo Vidal sending a couple of efforts over the bar from outside the box.
When Luis Jimenez did take a more penetrative approach and wriggle into the box after 38 minutes he was brought down heavily by a challenge from Martin Caceres. Replays showed the defender just got enough on the ball to avoid a spot-kick, but Suarez was unimpressed and his protestations earned him one of four first-half yellow cards.
The Liverpool man was a model of perpetual energy, floating across the width of the Uruguay attack, and exploited a loose pass from Chile to nip in behind the defence and round the keeper, only to see Diego Forlan struggle to leap to meet his cross and produce a weak header that was cleared off the line by Pablo Contreras.
It was an entertaining contest but, like the tournament itself, lacked goals. Chile went closest in the first half in fortunate circumstances when an attempted clearance from Sebastian Coates struck Mauricio Isla and looped back over the defender's head and against Fernando Muslera's bar.
Jean Beausejour finished another goalless half in Argentina by drilling a shot just wide of the post from a tight angle following a neat through-ball from Sanchez.
Chile started the second half with purpose and went close through an audacious backheel from Jimenez, but it was Uruguay who took the lead. Chile's defence were culpable when Suarez picked up a loose ball, rode a couple of challenges and cut the ball back for Alvaro Pereira, who was completely unmarked and gratefully slotted a low shot home.
Suarez was a sporadic threat and did well again when carrying the ball 35 yards, dodging one challenge, holding off another opponent and crashing in a shot that forced Bravo to parry behind for a corner. Sebastian Coates headed over from Forlan's set-piece though.
On 64 minutes Chile were level as Sanchez showed a glimpse of why the best club team in world football are pushing so hard to sign him from Udinese. After collecting a cut-back from Beausejour, Sanchez took a touch and then dug the ball out with a clinical toe poke that snuck away from Muslera.
The poacher almost turned provider soon after when Sanchez darted away from two markers in the box and picked out Jimenez with a glorious cross. His header had power but Muslera showcased his reflexes with a brilliant save on the dive.
Uruguay threw on playmaker Nicolas Lodeiro and forward Sebastian Eguren in an effort to snatch a crucial win, but Chile, sitting atop Group C, finished the stronger side as Mauricio Isla stung Muslera's hands with a fierce volley from long range.