Dunga's reign in charge of the South American powerhouse has now overseen two clean sheets, a far cry from conceding seven against the Germans at the World Cup.
However, the Brazilians still had their moments at the back against Sixto Vizuete's men, but they held firm for another narrow win courtesy of Willian's 31st-minute goal.
Dunga made just two changes to his starting XI from the side that beat 10-man Colombia on Friday, with Maicon - banished from the squad due to an "internal problem" - and David Luiz (knee) replaced by Marquinhos and Danilo.
Standing over the dead ball, Oscar played it short to Neymar - who had earned the free-kick - and the Barcelona star's lofted ball through found Willian who finished cleanly.
The West Ham forward got his head on a cross in from Sornoza in the 32nd minute, but it did not threaten Jefferson in goal.
Three minutes later, though, Valencia rattled the woodwork as Brazil's defence looked increasingly vulnerable.
And with a two-goal cushion high on Brazil's wishlist, Neymar blew a chance in front of an empty net early in the second half.
Valencia connected at the back post from a well-weighted cross from the right byline from Juan Paredes, but the goal-bound effort was first parried by Jefferson before Filipe Luis acrobatically cleared with the outside of his left boot.
However, Brazil's best chance to seal the match fell to Neymar - who was fouled on the edge of the area in the 80th minute.
However, the attacker's shot from the dead ball was deflected wide by Ecuador's Walter Ayovi - and was incorrectly ruled a goal-kick by central referee Edvin Jurisevic.
