The win in the southern city of Porto Alegre means coach Dunga, who replaced 2002 World Cup winner Luiz Felipe Scolari in the dugout after last year's World Cup semi-final thrashing by Germany, retains his perfect record.
There was precious little 'samba' football on offer as Roberto Firmino netted the only goal on the half hour.
Neymar did get a runout after the break but primarily to shake off any end of season lethargy after crowning a treble-winning campaign for Barcelona with Champions League glory in Berlin.
Yet the narrow win boosted morale ahead of the Copa America continental championship starting Thursday, when hosts Chile take on Ecuador.
Dunga led the 'auriverde' to the 2007 Copa title during a first spell in charge which ended with a 2010 World Cup quarter-final exit to the Netherlands.
Now he must blend a new generation of emerging stars with an experienced backbone after last year's catastrophic implosion to the Germans, who sauntered to a 7-1 win with Neymar out injured.
Sunday, the five-times world champions had beaten Mexico 2-0 in Sao Paulo in their first home game since last year's World Cup.
On that occasion, Neymar was excused altogether following his European Cup exploits with all-conquering Barca the previous day.
Dunga, Brazil's 1994 World Cup-winning skipper, will now take his squad to Chile to face Group C rivals Peru, Colombia and Venezuela.