Second-half goals from Eduardo Vargas and Alexis Sanchez saw Chile to a 2-0 win over Brazil in their World Cup qualifier on Thursday.
Vargas side-footed in a 72nd-minute goal at the Estadio Nacional Julio Martinez Pradanos in Santiago before Sanchez sealed it late on for the Copa America champions.
They had looked the more likely to score throughout, with Sanchez and Mauricio Isla hitting the post.
Brazil looked best on the counter-attack, but they rarely troubled Claudio Bravo on the opening day of CONMEBOL World Cup qualifying in South America.
Dunga's men felt the absence of suspended star Neymar, with Hulk struggling to get into the game.
The victory was just Chile's eighth in 71 meetings against Brazil and first since 2000.
While the win is an ideal start for Chile, Brazil need to respond when they host Venezuela on Tuesday.
Despite injury concerns surrounding Sanchez and Arturo Vidal, both started for Chile.
Of the starting XI that won the Copa America final in July, only Charles Aranguiz was missing – his place taken by Gonzalo Jara.
Brazil were without the suspended Neymar and injured pair Philippe Coutinho and Roberto Firmino, with Hulk starting up front.
Vargas threatened in just the fifth minute, but Jefferson was untroubled by the tame effort.
At the other end, Hulk scuffed a long-range free-wick wide, before Sanchez and Vargas combined for the latter to curl a 25-yard effort off target.
The opening half-hour was cagey as neither side managed to penetrate.
The closest either came to scoring was Sanchez's effort in the 42nd minute.
Vidal's flick and Mark Gonzalez's hard work created the chance for the Arsenal star, who hit the outside of the post on the turn.
The game opened up after the break and the hosts were denied by the woodwork once more.
Isla fired a powerful angled effort at goal from the edge of the area, but he too was denied by the outside of the post.
The hosts had another big chance in the 68th minute, but Gonzalez dragged his shot across goal after being played in down the left by Vidal.
But just four minutes later Chile were ahead.
Matias Fernandez's set-piece from the right was met by Vargas, whose side-footed effort proved too powerful for Jefferson.
Brazil almost levelled immediately as Ricardo Oliveira just narrowly missed out on getting on the end of Willian's low cross.
Chile would seal their win in the 90th minute as Sanchez and Vidal played a one-two, poked in by the former despite an initial block on the line.
