Remarkable comeback: Lazio were well in control of the tie, but Salzburg then scored three times in five crazy minutes through Amadou Haidara, Hee Chan-hwang and Stefan Lainer to secure a memorable 6-5 aggregate victory. PHOTO: AFP
Arsenal also reached the semi-finals after recovering from a wobble to draw 2-2 at CSKA Moscow and progress 6-3 on aggregate, while favourites Atletico Madrid reached the last four after losing 1-0 at Sporting to go through 2-1 over the two legs.
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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 but Salzburg equalised a minute later through Munas Dabbur.
Salzburg then scored three times in five crazy minutes through Amadou Haidara, Hee Chan-hwang and Stefan Lainer to claim a remarkable 6-5 aggregate victory and become the first Austrian side into a European semi-final since 1996.
Former European champions Marseille found themselves 2-0 down on aggregate inside two minutes at the Stade Velodrome when Leipzig's Bruma silenced the home crowd but they recovered to win 5-2 for a 5-3 aggregate win.
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Stefan Ilsanker's own goal put Marseille level on the night and the French club were ahead inside 10 minutes when a lighting counter-attack ended with Bouna Sarr firing home.
Marseille edged ahead in the tie for the first time when inspirational captain Dimitri Payet's whipped free kick was stabbed home by Florian Thauvin before halftime.
The visitors scored a second when Jean-Kevin Augustin's superb free kick turned the tie in Leipzig's favour again in the 55th minute but Payet's magical goal with the outside of his right foot on the hour sent the home fans wild.
Leipzig poured forward looking for the decisive away goal but Marseille's Hiroki Sakai broke clear in stoppage time to seal victory, firing into an empty net.
Arsenal took a commanding 4-1 lead to Moscow but trailed to goals from CSKA's Fedor Chalov and Kirill Nababkin and looked in danger of throwing away their advantage.
CSKA's fans, hundreds of whom watched shirtless from behind the goal, roared on their team but Danny Welbeck's well-taken goal calmed Arsenal's nerves, whereas Aaron Ramsey scored in stoppage time to complete the comeback for the Gunners.
Sporting made Diego Simeone's Atletico side suffer in the Portguese capital where Fredy Montero's 28th minute goal halved the Spanish club's first-leg lead.
However, Atletico held on to progress on aggregate after their striker Antoine Griezmann missed a hatful of chances and will take their place in Friday's semi-final draw.
Koscielny not happy despite progress to last-four
Arsenal captain Laurent Koscielny admitted his side came close to a Europa League meltdown at CSKA Moscow on Thursday where they recovered from two goals down to snatch a 2-2 draw and reach the semi-finals 6-3 on aggregate.
"It was not the plan. I think we missed a lot of movement, to be available for our team mates," Koscielny told BT Sport. "We didn't win duels. They played well, had opportunities and took them. It put pressure on us, if they score (a third goal) we are out. So I am happy because we came back, but our performance was not enough for the stage of the competition."
Arsenal are sixth in the Premier League and have little chance of qualifying for the Champions League via a top-four finish so the Europa League is their last hope.
"We will see the draw, but we need more confidence in our game," said the French defender. "It's our last chance to qualify for the Champions League, so we will fight until the end."
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