Nacional headed to Vasco's home ground in Rio de Janeiro two goals down from the first leg of their round-of-16 clash but struck from the penalty spot in just the seventh minute on Thursday to keep their hopes of progressing alive.
But Vasco recovered from the early blow and were level at half-time thanks to Marlone's strike, while Dakson gave the hosts victory in the 89th minute to wrap up a 4-1 aggregate win.
Internacional advanced with a 5-2 aggregate victory, despite being held to a 2-2 draw away to Salgueiro.
In Rio, Nacional stunned the home crowd when Erick Soares Rosa beat Vasco's Fillipe Soutto in the penalty area and then was brought down from behind by the midfielder.
Nacional's captain Danilo Rios had his spot kick saved by Vasco goalkeeper Diogo Silva but scored from the rebound to put the visitors ahead.
Vasco equalised in the 33rd minute when Victor Yotun got past his opponent on the left wing, burst into the area and then cut back to Marlone, who slotted his shot into the top corner.
In a tight second half, Vasco had to wait until the penultimate minute of normal time to win the contest.
A flowing move ended with Fabio Lima on the right-hand side of their attacking penalty box and he lifted a brilliant pass over a Nacional defender to fellow substitute Dakson, who poked the ball the home from a tight angle.
In Salgueiro, Internacional were pegged back twice by their Serie D hosts with the home side snatching a draw with an equaliser in second-half injury time.
Jorge Henrique scored the visitors' opener in the first half before Ranieri pulled Salgueiro level in the 57th minute.
Alex Raphael Meschini hit the back of the net five minutes later to give Internacional the ascendency again.
But in the 91st minute, Daniel Rodrigues Nazare slammed his left-foot shot past Internacional's goalkeeper Alisson to give the home side some joy despite their elimination.
Internacional and Vasco have joined Gremio, Atletico PR, Goias, Corinthians, Flamengo and Botafogo in the last eight.
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