Arturo Vidal scored a spectacular headed own goal while Victor Caceres and Richard Ortiz both netted to give Paraguay a vital win over the South American champions in Santiago.
The victory lifted Paraguay back into the South American qualifying race, leaving them in sixth place with 21 points from 15 games.
Chile remain in the automatic qualifying places with 23 points, but have little margin for error in an increasingly tight race.
The Chilean defeat capped an unhappy 24 hours for Arsenal star Sanchez, who had seen his hopes of a transfer deadline-day move to Manchester City collapse earlier Thursday.
Sanchez looked out of sorts throughout as Chile struggled to deal with a Paraguay side desperate for a win.
The Paraguayans grabbed the lead after 24 minutes when Oscar Romero swung a teasing free-kick into the Chilean penalty area.
Vidal leapt to clear but could only watch in horror as his thumping diving header crashed into the top corner.
It got worse 10 minutes after half-time as sloppy Chilean defending allowed Caceres to pounce on a loose ball to stab home his finish.
In time added on, Romero surged clear on the counter-attack as Chile pressed forward and released to Ortiz who took his time to drill a finish past Claudio Bravo.
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