Marcus Rashford's swerving strike from distance earned Manchester United a 1-0 win at Real Betis on Thursday and passage to the Europa League quarter-finals with a 5-1 aggregate triumph.
Three-time champions Juventus earned a 2-0 win over 10-man Freiburg to progress 3-0 on aggregate, with goals from Dusan Vlahovic and Federico Chiesa.
Record six-time winners Sevilla suffered a nervy 1-0 defeat at Fenerbahce as Enner Valencia netted from the spot, but still qualified 2-1 on aggregate.
Joaquin hit the post for Betis and Juanmi spurned two clear chances for the hosts as they started well, trying to overturn their three-goal deficit at the lively Benito Villamarin stadium.
However Rashford's brilliant goal early in the second half quelled that idea and United saw the game out comfortably as Betis' energy levels dipped.
"Once you score the first goal the game is gone, and they don't have the belief anymore," said Manchester United coach Erik ten Hag.
"That is another step (forward) we made mentality, a winning attitude, to deal with that."
Ten Hag handed 21-year-old winger Facundo Pellistri his first start for the club in sun-washed Seville, after some bright cameos from the bench.
After Juanmi's misses Pellistri came inches from putting United ahead, with his effort hitting the post.
The visitors took the lead early in the second half, through Rashford's thunderbolt.
The forward, in remarkable form this season, missed two fine chances after the break but swiftly made amends with a vicious shot from outside the area which flew past Rui Silva and into the bottom corner.
It was Rashford's sixth goal of the tournament and his 27th across all competitions this season, in 43 appearances.
"Rashy had some chances before, and he missed some but he kept his belief, he kept trying and got his reward," added Ten Hag.
United's coach had run a risk by lining up with Bruno Fernandes and Casemiro, who were each a booking away from suspension, but they survived unscathed.
"When we found out the draw, we knew we had the hardest opponent in the Europa League, with a huge budget, prepared for the Champions League," said Betis coach Manuel Pellegrini.
"In the second leg we had three clear chances to change the dynamic, while they had one and they stuck it in. But I am proud of my team, which did not change its identity."
Juventus, leading Freiburg by a goal from the first leg, thought they had taken the lead when Vlahovic struck from close range, but it was ruled offside by VAR.
However the Serbian forward broke the deadlock just before the break from the penalty spot after Manuel Gulde handled in the box and was shown his second yellow card.
With Juventus fully in control and Freiburg at a numerical disadvantage, the tie was as good as over and Chiesa wrapped up the win late on.
Jorge Sampaoli's Sevilla, struggling badly in La Liga, suffered defeat in Turkey but had done enough at home to progress against Fenerbahce and continue their charge.
Michy Batshuayi went off injured for the hosts early on, damaging their comeback bid, but Jorge Jesus' team took the lead when Alex Telles handled in the box.
Veteran Ecuador striker Valencia drilled home his 24th goal of the season for Fenerbahce.
Sevilla held out to progress despite pressure from the hosts in the second half, as they looked for a second goal to force extra-time.
Feyenoord thrashed Shakhtar Donetsk 7-1 on the night at De Kuip to progress to the last eight 8-2 on aggregate.
Later Thursday Arsenal host Sporting Lisbon after a 2-2 draw in the first leg, while Jose Mourinho's Roma hold a 2-0 lead over Real Sociedad as they visit San Sebastian.
In the UEFA Conference League last 16 Fiorentina thrashed Sivasspor 4-1, triumphing 5-1 on aggregate, while Lech Poznan beat Djurgarden 3-0 to go through 5-0 overall.
Later on West Ham host AEK Larnaca with a 2-0 lead and Villarreal welcome Anderlecht after sharing a 1-1 draw with the Belgians in the first leg.