Gremio avoided defeat in Porto Alegre, where the hosts snatched a draw thanks to substitute Pepe's 88th-minute equaliser on Wednesday.
Flamengo were superior for large spells in the all-Brazilian affair at Arena do Gremio – Jorge Jesus' visitors seeing three goals ruled out by VAR.
Bruno Henrique did give Flamengo the lead in the 69th minute after rising highest to head past Gremio goalkeeper Paulo Victor at his near post.
However, Pepe came off the bench to rescue Gremio during the closing stages midweek.
Everton fizzed a powerful effort across the six-yard box and team-mate Pepe was on hand to score with his thigh.
Flamengo will host the return leg in Rio de Janeiro on October 23.