Brazil continued their winning run under Dunga, but they left it late to get past Peru at the Copa America.
Douglas Costa scored a dramatic stoppage-time winner as Brazil overcame Peru 2-1 in their Copa America opener on Sunday.
Costa, a second-half substitute, netted in the 92nd minute after a wonderful Neymar pass.
In a frantic start at the Estadio German Becker in Temuco, Neymar and Christian Cueva both struck in the opening five minutes.
But Brazil left it late to make it 11 straight wins after the World Cup and under Dunga, who is in his second stint in charge.
Brazil and Venezuela are both on three points in Group C, with Peru and Colombia point-less.
Dani Alves, a late call-up to Dunga's squad, was handed a start, while Shakhtar Donetsk's Fred earned his spot in the talented attacking third.
But it was Peru taking a shock lead in just the third minute.
It looked like the Brazil of last year's World Cup as calamitous defending led to the opener.
A harmless long ball led to David Luiz trying to dribble across his own six-yard box and it turned into a pass to goalkeeper Jefferson, who turned over possession trying a short pass of his own.
Cueva was on hand to intercept before taking a touch and firing in from close range.
But Brazil were level just two minutes later thanks to Neymar.
Dani Alves, who caused plenty of problems down the right throughout the first half, crossed for the unmarked Barcelona star to head into the bottom corner.
Fred and Neymar fired wide soon after as the incredibly open start threatened to produce more goals.
Neymar almost put Brazil ahead in the 13th minute, only to see his close-range effort cleared off the line by Carlos Zambrano.
Diego Tardelli headed a tough chance over seven minutes later before the contest finally settled.
Neymar, who starred throughout, went close to making the breakthrough in the 53rd minute.
Peru failed to clear despite two opportunities, and Neymar whipped a 25-yard effort onto the crossbar.
Brazil looked the more likely to score and Costa squandered a great chance in the 75th minute, poking wide after Neymar put him through following a counter-attack.
But the goal would come on the counter, with Neymar's defence-splitting pass finding Costa to squeeze in a shot for the match-winner.