It was the Barcelona forward who made the vital contribution as Brazil broke the deadlock in the 31st minute through Willian, who found space inside the box to tap home his teammate's cross from a free kick.
Ecuador came agonisingly close to equalising just five minutes later when Enner Valencia watched his effort from a tight angle strike the post.
It should have been 2-0 in just the second minute of the second half, but Neymar could only hit the crossbar after Danilo had delivered an inviting cross into the six-yard box.
That close call appeared to help Ecuador, who tested Jefferson for the first time when Juan Cazares drilled the ball straight at the Brazilian goalkeeper.
Chances continued to be wasted by Ecuador, with Valencia heading straight at Jefferson from close range as Brazil were forced to withstand an extended spell of pressure from their South American rivals.
Brazil responded impressively following a slow start to the second half, and the introduction of Philippe Coutinho almost had an immediate impact as Marquinhos headed over from the Liverpool midfielder's cross.
An eye-catching cameo from Coutinho continued, but he was denied a first goal for his country when Alexander Dominguez blocked a powerful strike.
However, Brazil were not to be denied as Dunga watched his players taste success for the second time in a week.