Paris Saint-Germain held their nerve to beat Liverpool 4-1 on penalties and reach the Champions League quarterfinals on Tuesday after their tie finished one-apiece on aggregate, while Bayern Munich saw off Bayer Leverkusen to complete a 5-0 win over both legs.
Lamine Yamal and Raphinha fired Barcelona into the next round as the Catalans bested Benfica 3-1, and Inter Milan booked a last-eight meeting with Bayern by seeing off Feyenoord 2-1.
At Anfield, Ousmane Dembele netted the only goal of the night as PSG bounced back from Liverpool's late winner last week to force the tie to extra-time and penalties.
Maligned for his weak attempted save at the Parc des Princes from Harvey Elliott's strike, Italian goalkeeper Gianluigi Donnarumma produced two excellent saves in the penalty shoot-out to send the French champions into the last eight.
Donnarumma plunged first to his left to deny Darwin Nunez, before going low the other side to deny Curtis Jones, with his teammates dispatching all of their penalties.
"It was a great performance. We really deserved to go through over the two legs, hands down," PSG captain Marquinhos told Canal Plus.
The hosts dominated the opening exchanges but could not make their chances count, much like PSG in last week's return fixture.
Dembele poked home in the 12th minute after he reacted quickest to Ibrahima Konate's attempt to clear a PSG counter-attack in the Liverpool penalty box.
Jarell Quansah hit the post with a header in the second half, but PSG held firm under Liverpool pressure to claim the second leg 1-0.
The tie rumbled inevitably towards penalties and after Donnarumma's heroics, Desire Doue slammed home the decisive penalty to spark wild celebrations in the visitors' end.
"It was the best game of football I have ever been involved in," Arne Slot told Amazon Prime.
"It was an incredible performance, especially if you compare it with last week. We were creating chances and then we were 1-0 down. We ran out of luck after last week."
PSG will play either Aston Villa or Club Brugge in the next stage.
Harry Kane inspired Bayern to a 2-0 win at the home of German rivals Leverkusen.
The England captain scored and assisted at the BayArena, adding to his two goals from the comprehensive 3-0 first-leg victory in Munich.
"From the first minute we didn't want to be a team that dropped off and tried to defend the lead," Kane told Amazon Prime.
"In the second half we knew they had to come out and try something and we punished them."
With the match scoreless at halftime, Bayer pushed to try and get a foothold in the tie in the final 45 minutes.
But it was Kane who tapped in from a lofted Joshua Kimmich cross in the 52nd minute to kill off the tie.
Alphonso Davies made it a rout over both legs with 19 minutes remaining as he drove home a chipped pass from Kane.
"We didn't lose the tie today," said Leverkusen coach Xabi Alonso. "We made it too difficult for ourselves in the return leg."
'WIN EVERYTHING'
Already a goal to the good following the first leg, a Raphinha brace and a Yamal wonder-goal secured Barca a 4-1 aggregate win on Tuesday.
Hansi Flick's side will face Borussia Dortmund or Lille in the quarterfinals as they aim to win the competition for the first time since 2015.
"We are candidates to win everything," Raphinha told Movistar, with the club in the hunt for a potential treble.
Teenage sensation Yamal created the opener on 11 minutes with a mazy run before his mishit shot picked Raphinha out perfectly as the Brazilian ghosted in at the far post.
Nicolas Otamendi struck back instantly for Benfica when he forced a header past Wojciech Szczesny in the 13th minute.
Yamal restored the home side's two-goal buffer 14 minutes later, cutting in from the right flank and arching an unstoppable effort into the far, top corner.
Raphinha then put the tie to bed three minutes before the interval with a blistering left-footed finish following excellent work by Alejandro Balde.
The build-up to the match at the Olympic Stadium was overshadowed by the sudden death last Saturday of Barcelona club doctor Carles Minarro, and the players observed a silence in his honour before kick-off.
"We won for us and Carles is always with us... he always has a place (here)," said Flick.
Italian champions Inter also progressed through the last 16 with a 4-1 aggregate victory.
Strikes by Marcus Thuram and Hakan Calhanoglu, either side of a Feyenoord consolation scored by Jakub Moder, gave them a 2-1 win at the San Siro.
Thuram's fierce eighth-minute strike put the Nerazzurri into a commanding 3-0 aggregate lead, before Moder and Calhanoglu both scored from the spot shortly before and after the interval.