Fans of Universidad, holders of the lesser Copa Sudamericana, feared their attractive, attacking side had blown their chances at high altitude in Ecuador last week but "La U" bushed Deportivo aside to go through 7-4 on aggregate.
There were two goals apiece from midfielder Junior Fernandez and striker Angelo Henriquez as the Chileans progressed to a quarter-final clash with Paraguay's Libertad while the Ecuadoreans paid the price for trying to defend their first-leg advantage.
Santos' home victory at the Vila Belmiro gave them a 9-2 aggregate win after they were beaten 2-1 by the Bolivian side in the thin air of La Paz in the first leg two weeks ago.
Three times South American champions Santos will meet 1994 winners Velez Sarsfield of Argentina in the quarter-finals.
Inspirational striker Neymar and midfielders Elano and Paulo Henrique Ganso, who netted a brilliant free-kick, all scored twice.
In one astonishing sequence on the left wing, Neymar let a long ball out of defence bounce off his back and land perfectly for a team-mate, then received the return, stepped over the ball and flipped it over his head to himself before passing it again.
Fluminense beat twice champions Internacional 2-1 in a much tighter all-Brazilian last-16 tie at the Engenhao in Rio de Janeiro for an aggregate victory by the same score.
Headed goals by Leandro and Brazil striker Fred in the first half cancelled out an early opening Inter strike by Leandro Damiao.
Fluminense, looking to win the trophy for the first time, clash again with six times champions Boca Juniors in the last eight after meeting in the group phase when Flu beat Boca 2-1 away but then lost 2-0 at home to the Argentine side.
Corinthians, another major Brazilian side yet to lift the trophy, meet 1998 champions Vasco da Gama in the other quarter-final after both qualified on Wednesday.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.