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.
Vizuete also made two changes from the side that thrashed Bolivia 4-0 on Saturday, goalkeeper Alexander Dominguez and attacker Junior Sornoza starting in place of Maximo Banguera and Fidel Martinez respectively.
Brazil led after a fine move from a set piece on the half-hour mark.
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.
Ecuador responded admirably, with Enner Valencia twice threatening to equalise.
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.
Neymar, the match-winner against Colombia on Friday, got his foot to a low cross in from the right, but he poked it into the underside of the crossbar - and it deflected back into the grateful hands of Ecuador custodian Dominguez.
Ecuador continued to press and bother the Brazilian defence, and they had few better chances than a header from Valencia again - which was cleared off the line by Filipe Luis in the 61st minute.
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.
The game was end-to-end for much of the second half, with Dunga swinging five changes throughout the period as he trialled the likes of Fernandinho, Elias, Philippe Coutinho, Ricardo Goulart and Everton Ribeiro.
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.
It did not matter, though, as Brazil made it back-to-back victories since their calamitous World Cup campaign ended with consecutive heavy defeats.
