The result means Ecuador have one point from two games in Group B and Venezuela have two points from three.
Ecuador and Venezuela are the only teams in South America never to have won the Copa America and although the game in Rio did not lack goalmouth action the quality of football on show did not suggest that might change this year.
Ecuador had two-thirds of both the possession and shots on goal but struggled to turn that dominance into something more meaningful against a stuffy Venezuela.
They had not lost to Venezuela for six games dating back to 2011 and controlled the first half before going ahead six minutes before half-time when Ayrton Preciado scrambled a goal inside a packed six-yard box.
Edson Castillo bulleted home a header after 51 minutes to equalise on his first international start for Venezuela only for Ecuadorian substitute Gonzalo Plata to race the length of the field and give his side a 2-1 lead with 19 minutes remaining.
Enner Valencia should have cemented the victory when he only had the keeper to beat 12 minutes from time but the Fenerbahce striker put his shot wide.
Just when it looked like Ecuador would escape with all three points Hernandez got on the end of a 40-meter pass into the box to loop a header past the stranded keeper.