Salzburg forced Lazio into a second-half capitulation as the Italians crashed out in the Europa League quarter-finals after losing 4-1 but Olympique de Marseille staged a thrilling fightback to see off visitors Leipzig 5-2 on Thursday.
Bookies' favourites, Atletico Madrid also lost 1-0 to Sporting Lisbon in Portugal but advanced after winning the first leg 2-0 in Spain.
Elneny then sent Ramsey - scorer of a brace in the first leg - away to score Arsenal's equaliser on the night in stoppage time.
"It should be every year".
"Everybody speaks about Atletico Madrid".
Koke put Atletico in front after only 23 seconds of the first leg but they were on the back foot in the early stages in Lisbon. "They were mobile and technically good and they gave us many problems".
They'll be trying to emulate city rivals Roma, who shocked Barcelona to enter the Champions League semi-finals, and don't hold back ahead of Sunday's Derby della Capitale showdown in Serie A. "We were close to a comeback but we were not close enough".
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Lazio led 4-2 from the first leg in Rome and increased their advantage when Ciro Immobile scored his eighth goal in this season's competition in the 55th minute.
Amadou Haidara's 72nd-minute strike from 30 yards sparked an fantastic four-minute period, in which Hwang Hee-chan put the Austrian champions ahead on away goals before Stefan Lainer headed an aggregate victor.
Former European champions Marseille found themselves 2-0 down on aggregate inside two minutes at the Stade Velodrome in the south of France when Leipzig's Bruma silenced the home crowd but they recovered to secure a 5-3 aggregate win.
With the Germans sending everyone forward for a corner in stoppage time, Marseille made sure of the victory as Hiroki Sakai netted on the counter-attack to complete a 5-3 aggregate win.
Fredy Montero's headed home in the first half for the game's only goal in the second leg, but Los Rojiblancos progressed after winning 2-1 on aggregate.
Atletico's possible opponents in Friday's semi-final draw are Salzburg, Arsenal and Marseille.