Substitute Marcos Bolados scored in the 90th minute to propel Chile to a 2-1 victory in Sweden on Saturday.
Arturo Vidal had given Chile the lead midway through the first half by sending a volley into the roof of the net.
But the hosts struck back inside a minute, however, as Ola Toivonen scored after receiving a touch pass from Viktor Claesson.
Bolados then tapped home a rebound after Kristoffer Nordfeldt had saved a shot from Alexis Sanchez for the late winner.