Palestino, who ended the match with nine men, were 2-1 winners over Cobresal in the return leg at the Estadio Municipal de La Cisterna.
However, Cobresal's solitary goal in the second half was enough for Jose Cantillana's men to triumph 3-2 on aggregate after Wednesday's 2-0 win in the opening leg in front of their home fans.
Palestino always faced an uphill task after falling two goals behind at the end of the first leg and the odds were stacked against them even more when Argentinian midfielder Sergio Lopez saw red in the 36th minute.
Despite playing with a man less, the home side took a surprise lead through Esteban Carvajal, who broke the deadlock on the stroke of half-time.
But just as Palestino started to build some momentum, they were dealt a major blow following Renato Ramos' dismissal, which reduced the hosts to nine men with 34 minutes still remaining.
They showed tremendous fighting spirit to push on and double their advantage on the hour mark, with defender Rodrigo Riquelme the unlikely goalscorer.
However, that was as good as it got as Felipe Salinas scored the crucial away goal in the 68th minute to give Cobresal victory on aggregate.
