In a largely turgid affair, the Hoffenheim man replaced the ineffective Luiz Adriano on the hour-mark, and struck the winner with a coolly-taken finish 11 minutes later.
The clash saw two of the modern game's biggest superstars in opposition, but neither Neymar nor Alexis Sanchez - on his home ground - had a significant impact.
Sanchez did show some touches of brilliance, while Neymar was involved in the game's most controversial moment in the first half when Chile midfielder Gary Medel stood on his leg in an off-the-ball incident which went unseen.
The two sides' previous meeting came in the round of 16 in last year's World Cup, a game which saw Brazil prevail on penalties.
This encounter had none of that drama, but that will be of little concern to Brazil, who extended their perfect start to Dunga's second stint in charge, with eight victories from as many games since those fruitless finals on home soil.
After an uneventful opening 20 minutes, Medel was fortunate to remain on the field after standing on Neymar as the pair tangled.
In getting back to his feet, Medel trod on the calf of the Brazil man, leaving Neymar writhing on the ground in apparent agony, but referee Martin Atkinson seemed not to see the incident.
Brazil went close to an opener in the 26th minute when Neymar's free-kick from the left eluded everyone and had to be tipped round the post by Barcelona colleague Claudio Bravo.
Eight minutes prior to the interval, Marcelo's diagonal ball picked out Douglas Costa unmarked at the back post but, after chesting the ball down, his volley was wayward.
Chile felt they should have had a penalty 11 minutes into the second period when Mauricio Isla went down under Marcelo's challenge, but Atkinson waved away their appeals.
Sanchez, having been hauled down by Miranda, curled a 25-yard free-kick narrowly over the bar in the 64th minute before firing another set-piece straight at Jefferson as Chile looked the more likely side to break the deadlock.
However, somewhat against the run of play, it was Brazil who went in front as Danilo's pass picked out Firmino, who rounded Bravo and slotted home – cheekily looking away in the process of scoring.
Chile were unable to force an equaliser in the closing stages, as Brazil held on and gave themselves a boost in their final game before the deadline to announce squads for the Copa America in June, with Firmino looking increasingly likely to be involved.
