Benfica survived a dramatic late onslaught in Lisbon to reach the quarter-finals with a 2-2 draw having won the first leg 3-1 at White Hart Lane last week.
Jorge Jesus's team appeared to be cruising towards the last eight when Ezequiel Garay scored in the first half at the Estadio da Luz.
But Nacer Chadli struck twice in quick succession late in the second half to give Spurs hope of forcing extra-time.
Benfica barely managed to hold out before Rodrigo Lima's penalty in stoppage-time sealed a 5-3 aggregate success which secured the Portuguese club's spot in Friday's quarter-final draw.
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"I think it's evident the players are on my side. They have showed real character and real guts and they need to do that until the end of the season.
"It was good to see their manager sweating. I did not see a suave character on the side, I thought someone who was really flustered, which was good to see."
An Andrea Pirlo free-kick secured Juventus's ticket to the quarter-finals after a 1-0 win over 10-man Serie A rivals Fiorentina.
Fiorentina had high hopes of making the last eight after a 1-1 draw in Turin last week when Mario Gomez levelled Arturo Vidal's third-minute strike.