The 29-year-old is Dunga's chosen replacement for Fred, following Brazil's woeful World Cup elimination and the striker opened his international account at the Bird's Nest Stadium in Beijing.
Largely against the run of play, Brazil had the lead after 28 minutes when Tardelli scored his first Brazil goal - volleying home from inside the area after questionable Argentina defending.
Neither Pablo Zabaleta nor Federico Fernandez could clear Oscar's cross, with Tardelli taking full advantage, scoring more than five years after making his international bow to send Argentina on their way to a first defeat under Gerardo Martino.
Lionel Messi spurned the chance to draw Martino's men level before the break, his penalty saved by Jefferson, and Tardelli put the game beyond doubt with a second after 64 minutes.
The Atletico Mineiro man headed in from close range as he bolstered his claim to lead Brazil's line ahead of the Copa America in Chile next year, wrapping up a third consecutive Superclasico in the process.
Argentina started the brighter, with Sergio Aguero seeing an early penalty shout turned down when he went down under a challenge from Miranda.
With Martino's men continuing to dominate in the early stages, Angel di Maria fired over the crossbar following clever link-up play with Erik Lamela.
However, Brazil began to grow into the game shortly before the half-hour mark and took the lead through Tardelli's smart volley.
When Zabaleta and Fernandez failed to clear Oscar's delivery, Tardelli peeled away and fired home the loose ball unmarked, with Sergio Romero not doing enough to keep it out.
Neymar spurned an opportunity to level when one-on-one with Romero before Messi missed the chance to send Argentina in level at the interval.
Danilo was rather harshly adjudged to have brought down Di Maria but Messi saw his penalty saved by Jefferson with Marcos Rojo failing to divert the follow-up home.
Filipe Luis blazed Neymar's clever pass over the crossbar before Di Maria was uncharacteristically pedestrian when through on goal after Miranda lost possession - allowing the Atletico Madrid centre-back time to recover.
As in the first half, Argentina soon began to dominate possession but conceded against the run of play when Tardelli added his second shortly after the hour mark.
When David Luiz flicked on Oscar's corner, Tardelli was again unmarked as he stooped to head his second of the game and wrap up a third win from as many games under Dunga.
Tardelli was replaced by the returning Kaka, who made his first appearance since March 2013, having helped continue Brazil's positive start to Dunga's second tenure in charge while also leaving Martino with plenty to ponder.
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