Ecuador twice took the lead through Ayrton Preciado and Gonzalo Plata either side of a powerful headed goal from Venezuela's Edson Castillo.
The point left Venezuela third in the five team group on two points, one point and one place above Ecuador, who have a game in hand.
Hosts Brazil lead the group with a perfect two wins from two while Peru, who play Colombia later on Sunday, prop up the table.
Ecuador were off to a bright start with both Leonardo Campana and Enner Valencia shooting narrowly wide from good scoring positions.
Cristian Casseres was Venezuela's main threat but he skied one great chance from 12 yards out, before breaking the offside trap and seeing his chip over goalkeeper Pedro Ortiz cleared off the line by Pedro Hincapie.
The deadlock was broken in scrappy circumstances six minutes before halftime.
Pervis Estupinan sent a freekick into the box that Campana won in the air, causing havoc before Preciado stabbed home the loose ball after it ricocheted off goalkeeper Wuilker Farinez.
Venezuela were level, though, just six minutes into the second half when Castillo rose unmarked eight yards out to plant a bullet header from Jose Martinez's cross into the top corner, leaving Ortiz rooted to his line.
Three minutes later, Farinez got down quickly to save a header from Campana as Ecuador looked to hit back immediately.
They did move back in front 19 minutes from time after a length of the field counter-attack from a Venezuela corner.
Plata ran from one box to the other with the ball and although Farinez saved his tired effort, Christian Noboa's follow-up ricocheted back to him off a back-tracking defender and Plata poked home.
Soon after, captain Valencia had a chance to wrap things up but shot wide with only Farinez to beat.
After his earlier heroics, Plata was at fault for Venezuela's equalizer, caught out of position as Hernandez ran past him to head Edson Castillo's long ball into the box past a stranded Ortiz.