Sanchez had risked the wrath of Arsenal boss Arsene Wenger after playing in the Santiago showdown despite injuring a hamstring during training last week.
Wenger had expressed fear Chile had made a "suicidal" decision by playing Sanchez against the Uruguayans after the injury.
But the in-form striker showed no sign of ill-health with two second-half goals to seal Chile's comeback victory after Edinson Cavani had given Uruguay an early lead at the Estadio Nacional.
Uruguay dominated for long periods of the first half, with the movement of Luis Suarez and Cavani troubling Chile's defence.
The contest was a rematch of the two sides stormy collision at the same venue during the 2015 Copa America, when Uruguay finished the game with nine men after the infamous clash between Cavani and Gonzalo Jara.
Jara, who was later handed a two-match ban for appearing to shove a finger into Cavani's backside, was back at the heart of the Chilean defence on Tuesday alongside Gary Medel.
However Jara and Medel were both found wanting in the 16th minute when Uruguay took the lead through Cavani.
After hesitation between Jara and Medel, Suarez pounced on a loose ball and surged forward menacingly before rolling a pass into the path of Cavani.
The Paris Saint-Germain striker took the faintest of touches before rifling home an unstoppable shot past Claudio Bravo.
It was Cavani's eighth goal of the qualifying campaign, leaving him two clear of Arturo Vidal and Ecuador's Felipe Caicedo who have six each.
Uruguay looked to be heading into half-time 1-0 up but in stoppage time, Chile mounted their best attack of the half.
Sanchez released Jean Beausejour down the left flank and the former Wigan winger's cross found Eduardo Vargas who headed past Fernando Muslera for 1-1.
Chile came out for the second half clearly buoyed by the goal and on 60 minutes Sanchez struck.
The Arsenal forward spun away from Matias Vecino with ease on the edge of the area before getting his shot away.
Sanchez's effort was struck firmly but poor goalkeeping from Muslera allowed the shot to squirt into the net at the near post.
In the 76th minute, Sanchez then darted onto a long ball from Marcelo Diaz to make it 3-1.
In the closing stages Bravo denied Uruguay a lifeline when he saved a Suarez penalty.