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.
“We had them where we wanted them. They were running scared, weren’t they?” said Spurs manager Tim Sherwood.
“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.”
Benfica coach Jorge Jesus, who clashed with Sherwood in London last week, said: “We knew Tottenham could do what we did in London.
“We had five players not used to playing 90 minutes, but it was a risk we took because our objective is to win the Portuguese championship.”
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.
But the Florence-based side, who are the only team to have beaten Juventus in Serie A this season, failed to capitalise on what was a poor performance from Juve before the interval.
– Rodriguez red-carded –
Fiorentina suffered a huge blow on 68 minutes when defender Gonzalo Rodriguez saw red for a second bookable offence after hauling down Fernando Llorente on the edge of the area.
It gave Juve a free-kick in Pirlo’s preferred territory and the Italian playmaker smashed the ball past Brazilian ‘keeper Neto and into the top right-hand corner.
“I am really happy to make the quarter-finals, it’s another important step towards the final in our own stadium,” said Pirlo, who was hailed by fellow midfielder Paul Pogba.
“His foot, as I always say, is golden. To do what he does I’m going to have to train for many years,” said the Frenchman.
Napoli’s hopes of joining the Italian champions in the last-eight were ended by Porto when a 2-2 draw in Naples gave the Portuguese side a 3-2 aggregate win.
Goran Pandev gave Rafael Benitez’s Napoli a 21st-minute lead but Nabil Ghilas came off the bench to level in the 69th minute for Porto.
Ricardo Quaresma ended Napoli’s hopes when he dribbled round Valon Behrami and Gokhan Inler to drive into the roof of the net in the 76th minute.
Substitute Duvan Zapata levelled for Napoli at the death but Porto, 1-0 winners in Portugal last week, went through.
Dutch side AZ Alkmaar drew 0-0 at Russia’s Anzhi Makhachkala to go through 1-0 on aggregate while Valencia enjoyed a 1-0 home win over Bulgaria’s Ludogorets Razgrad for a 4-0 aggregate score.
French side Lyon lost 2-1 at Viktoria Pilsen in the Czech Republic but still went into the quarter-finals 5-3 over the two legs.
In Spain, Sevilla overturned a 2-0 first leg deficit to draw 2-2 on the night with city rivals Real Betis before taking the tie 4-3 on a penalty shoot-out.
In the night’s other tie, 10-man Basel came from behind to beat FC Salzburg 2-1 in Austria.
Basel’s Marek Suchy was red-carded in the ninth minute but Marco Streller (50 minutes) and Gaston Sauro (60) scored from second-half set pieces to cancel out Jonatan Soriano’s 22nd-minute volley.
The draw for the quarter-finals takes place on Friday with the ties on April 3 and 10.