Dynamo Kiev cracked opened the Everton defence to overturn a first-leg deficit with a 5-2 win and advance to the Europa League quarterfinals 6-4 on aggregate.
The game went back and forth in the first half with Andriy Yarmolenko drawng the hosts level in the 21st minute. Romelu Lukaku scored eight minutes later to put Everton back in front, but Lukasz Teodorczyk's goal in the 35th minute brough the tie level.
Two more Dynamo Kiev goals followed in the second half, Oleg Gusev tapping home a loose ball in the box and Antunes scoring from long range.
Phil Jagielka got one back for the visitors but that would be all for Everton, who were the last English Premier League team alive in European competition after Arsenal and Manchester City crashed out of the Champions League this week.
Brilliant Fiorentina stunned Roma with an early goal blitz to win 3-0 and seal their spot in the quarterfinals at the expense of their Italian rivals.
Roma might have held a narrow advantage after drawing the first leg 1-1 in Florence but any hopes of progressing were sunk inside 21 minutes on Thursday as Gonzalo Rodriguez, Marcos Alonso and Jose Maria Basanta all netted for Fiorentina.
The visitors might have extended their lead further in the second half, Mohamed Salah hitting the woodwork twice, but in the end the 3-0 scoreline was more than enough to send them through as sorry Roma finished with 10 men following Adem Ljajic's late dismissal.
Wolfsburg added to their advantage from the first leg to win 2-1 at Inter Milan for a 5-2 aggregate victory.
Daniel Caligiuri scored in the first half to give the Bundesliga side a three-goal lead on aggregate, and Inter could not respond until the 72nd minute when Rodrigo Palacio broke through.
Nicklas Bendtner scored Wolfsburg a late winner on the night in the 89th minute, though the tie was already well in hand.
Europa League holders Sevilla beat fellow La Liga side Villarreal 2-1 to advance 5-2 on aggregate.
Vicente Iborra scored in the 69th minute to give Sevilla an extra boost after their 3-1 win at Villarreal last week, and although Giovani dos Santos scored soon after, a second yellow card to Eric Bailly in the 77th minute greatly ended the visitors' slim hopes.
With advancement already nearly assured, Denis Suarez won the game late on for Sevilla.
Napoli are also through to the quarterfinals after a hard-fought goalless draw against Dinamo Moscow in Russia.
The Italians held a 3-1 lead from the first leg and that proved sufficient as they survived a second-leg onslaught from Stanislav Cherchesov's men.
Napoli hit the woodwork twice in the early stages as they looked to put the tie to bed but neither side could break the deadlock.
Torino's late push fell short and despite a 1-0 win they were eliminated by Zenit St. Petersburg 2-1 on aggregate.
The Russian side held the hosts without a goal until stoppage time when Kamil Glik was able to break through, but Torino could not find a second to force extra time.
Ukraine will have two teams in the quarterfinals after Yevhen Konoplyank's goal for Dnipro Dnipropetrovsk in extra time allowed them to advance past Ajax on away goals despite a 2-1 defeat on the night.
Trailing 1-0 from the first leg, Ajax fought back through Riechedly Bazoer's goal on the hour mark. But Konoplyanka's goal in extra time gave them the crucial away goals advantage, and though Mike van der Hoorn got one back for the hosts in the 117th minute, they could not find a winner.
Club Brugge rallied past Besiktas in the second half for a 3-1 win in a hostile atmosphere in Turkey to reach the quarterfinals 5-2 on aggregate.
Ramon Motta put the hosts ahead in the 48th minute, but the Belgian side went on to score three more times through Tom De Sutter and a brace from Boli Bolingoli-Mbombo.