Pineida struck in the 80th minute at the Estadio General Ruminahui del Valle de Los Chillos in Sangolqui, Ecuador.
Estudiantes, four-time champions, need a win when they host the second leg on February 12.
The Argentines looked set to hold on for a draw away from home until Pineida rifled in the winner.
The 22-year-old cut inside from the left, holding off a marker before firing into the top corner from 25 yards to help Independiente del Valle take a huge step towards the group stages.
Nacional, three-time winners of the tournament, went down 1-0 at Palestino.
Diego Rosende was the hero for the Chilean hosts, netting in the 70th minute in Santiago de Chile.
But a 35th-minute red card to Nacional defender Diego Polenta proved costly for the visitors, who were eventually punished.
Rosende found the bottom corner from just inside the area after a nice touch from Diego Chaves set up the chance.
