With Brazil's place in the knockout stages already secured before the clash at the Estadio Olimpico Pedro Ludovico, manager Tite opted to make 10 changes to the side that beat Colombia three days ago, with only captain Marquinhos keeping his place.
Eder Militao put the Selecao ahead shortly before half-time, but Ecuador improved after the break and deservedly sealed a point through Angel Mena.
Brazil will play the fourth-placed team in Group A in the quarter-finals, while Ecuador will play the winner of that group a day later.
The much-changed Brazil starting XI struggled in the early stages, only testing Ecuador goalkeeper Hernan Galindez through Gabriel Barbosa inside the opening 20 minutes.
Lucas Paqueta steered an effort wide from the edge of the penalty shortly after the midway point of the first half as Brazil started to exert more pressure on their opponents.
The Selecao's improvement was rewarded eight minutes before the interval when Militao headed home his first Brazil goal from Everton's free-kick.
Ecuador drew level in the 53rd minute, though, substitute Mena firing past Alisson from 10 yards after latching onto Enner Valencia's headed pass.
Substitute Vinicius Junior missed a glorious opportunity to restore Brazil's lead in the 66th minute, skewing wide at the back post from Paqueta's cross.
The defending champion rarely looked like finding a winner in the closing stages as Brazil's run of 10 consecutive wins came to an end with a whimper.