Nacional held Palmeiras of Brazil to a scoreless draw at Montevideo's Centenario stadium on Wednesday to go through on the away goals rule following a 1-1 stalemate in Sao Paulo in the first leg.
There was an identical outcome to the day's other quarter-final in southern Brazil, where twice champions Gremio were held 0-0 at home by Caracas FC but advanced on the away goal they scored in a 1-1 draw in the first leg in Venezuela.
Palmeiras dominated in Uruguay but squandered two good chances in the final minutes when Nacional keeper Rodrigo Munoz dived to save from Diego Souza and unmarked substitute Obina headed wide from six metres out with the goal at his mercy.
Santiago Garcia could have calmed Nacional's nerves four minutes from time when he broke clear of two defenders and steered the ball past Marcos, but watched as it skimmed the outside of the keeper's left hand post.
In the semi-finals, Nacional will meet either fellow Uruguayan side Defensor Sporting or Argentine three-times winners Estudiantes, who meet on Thursday in La Plata.
The Caracas players appeared to be treating their appearance at the packed Olimpico in Porto Alegre, awash with Gremio's blue and black colours, as a visit to a monument, taking pictures of each other on the pitch before kickoff.
In the end, however, defender Gabriel Cichero almost snatched an unlikely win with a late header that would have made them the first Venezuelan team to reach the last four in South America's equivalent of the UEFA Champions League.
Gremio now face an all-Brazilian semi-final against either Sao Paulo or Cruzeiro.
