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.
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.
Lazio, who are third in Serie A, 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.
With 19 minutes remaining Lazio still led 5-3 on aggregate but Salzburg scored three times in five crazy minutes through Amadou Haidara, Hee Chan-hwang and Stefan Lainer to claim a remarkable 6-5 aggregate victory.
They are the first Austrian side to reach a European semi-final since 1996 and are now unbeaten in 25 home games in all competitions this season.
"These are indescribable feelings of happiness," midfielder Xaver Schlager said. "We always believed in it, and that makes a lot of difference. These are wonderful moments for a player."
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.
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.
Jean-Kevin Augustin's superb curled finish turned the tie in Leipzig's favour again in the 55th minute but Payet's magical shot into the top corner with the outside of his right foot on the hour sent the home fans in the 60,000 sell-out crowd wild.
Leipzig poured forward looking for the decisive away goal but Marseille's Hiroki Sakai broke clear in stoppage time to wrap up the victory, firing into an empty net after Leipzig keeper Peter Gulacsi had gone forward for a corner.
Marseille, who are fourth in Ligue 1, have reached their first European semi-final in 14 years.
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. Aaron Ramsey scored in stoppage time to complete the comeback for the Gunners.
"It wasn't comfortable, we have seen in Europe how difficult it can be coming into games with an advantage," Welbeck said.
Sporting made Diego Simeone's Atletico side suffer in the Portuguese 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.