Pierre-Emerick Aubameyang spearheaded Arsenal's revival by scoring twice in a 3-0 win over Rennes to reach the Europa League quarter-finals 4-3 on aggregate, as Chelsea and Napoli also booked a last-eight spot on Thursday.
However, Rennes had cause to complain as Aubameyang should have been flagged offside before the second goal.
With VAR not in use for the Europa League unlike the Champions League, there was no recourse for Rennes and the Ligue 1 side will also reflect on missed opportunities after the break as a historic European run for the club came to an end.
M'Baye Niang struck the post and Sead Kolasinac's last-ditch tackle denied Ismaila Sarr before the Bosnian wing-back crossed for Aubameyang to give Arsenal breathing space.
But Arsenal boss Unai Emery, who won the Europa League three times as Sevilla coach, also wants the glory of a trophy in his first season in charge.
"It is not only the possibility to go to Champions League, it is one title and we can feel the possibility to win one title," said the Spaniard.
Chelsea cruised into the last eight with greater ease as six Premier League sides will take their place in Friday's quarter-finals draws with Manchester City, Manchester United, Liverpool and Tottenham in the last eight of the Champions League.
"We started very well. We wanted to start in this way," Chelsea manager Maurizio Sarri told BT Sport. "We played a wonderful first half and managed the game in the second half."
Giroud, who is yet to start in the Premier League in 2019 after the signing of Gonzalo Higuain, netted a first-half double, before Marcos Alonso slid home a third on the stroke of half-time.
- Sevilla shocked by Slavia -
Five-time winners Sevilla were beaten 4-3 after extra time to lose a thrilling tie against Slavia Prague 6-5 on aggregate.
However, after Franco Vazquez had given Sevilla a 3-2 lead on the night, Slavia hit back and Ibrahim Traore's winner a minute from time sealed a famous win for the Czechs.
Napoli wrapped up a 4-3 aggregate victory over last season's semi-finalists Salzburg despite a 3-1 second-leg loss in Austria.
Another Serie A giant fell, though, as the highly-rated Luka Jovic scored the only goal of the night and the tie as Eintracht Frankfurt beat Inter Milan at the San Siro. Russian outfit Krasnodar suffered heartbreak as Goncalo Guedes scored a dramatic injury-time equaliser to send Valencia through 3-2 on aggregate after a 1-1 second-leg draw.
Spanish sides have dominated this competition in recent years and despite Sevilla's defeat will have two representatives in the last eight as Villarreal beat Zenit St Petersburg 2-1 to seal a resounding 5-2 aggregate victory.
Benfica, runners-up in 2013 and 2014, were also taken to extra-time by Dinamo Zagreb but eventually overturned a 1-0 first leg deficit with a 3-0 win in Lisbon.
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