The Hoffenheim forward continued the impressive start to his senior international career in an otherwise rusty performance that saw coach Dunga visibly frustrated on the sidelines in Porto Alegre.
Firmino struck in the 33rd minute after a rampaging run down the left from Filipe Luis, latching onto the Chelsea defender's through pass to finish smartly between the legs of Honduras goalkeeper Noel Valladares.
Since making his debut in November, Firmino has played six matches for Brazil and scored three goals.
Wednesday's win was Brazil's 10th in a row and comes just three days after they saw off Mexico 2-0 in Sao Paulo.
It also saw Dunga maintain his perfect record in his second stint in charge since taking over after last year's World Cup.
The hosts became more dominant as the match wore on at the Estadio Jose Pinheiro Borda, finishing the game with 65 per cent possession and 15 shots to Honduras' seven, but were unable to build on their lead.
Honduras made it difficult for the home side by adopting a physical approach, with the visitors conceding 22 fouls, though Dunga will want to see more a cutting edge from his side when his team start their Copa America campaign against Peru on Sunday.
Captain Neymar returned after missing the match with Mexico due to his club commitments with Barcelona and was introduced at half-time.
With the CONCACAF Gold Cup looming next month, Honduras coach Jorge Luis Pinto has just one more friendly to prepare his team, as they host Mexico on July 1.