Borussia Dortmund staged a sensational stoppage-time recovery as they scored twice to beat Malaga 3-2 at home and book a place in the last four of the Champions League.
Last season's Bundesliga champions looked dead and buried after a sublime effort from Robert Lewandowski was sandwiched between goals for the Spanish club from Joaquin and substitute Eliseu.
However, Marco Reus gave the hosts a lifeline with a scrappy goal deep into added time before Felipe Santana sent the crowd into raptures when he fired in from what appeared to be an offside position following an almighty goalmouth melee.
It means Dortmund are into their first Champions League semi-final in 15 years and brings a heartbreaking end to a magnificent maiden campaign for Manuel Pellegrini's side, who will feel truly aggrieved by the manner of their exit.
Malaga's hopes had already suffered a major blow in the run-up to the clash as a heavy loss in La Liga, an aircraft scare and the death of coach Pellegrini's father all appeared to suggest their preparations had been seriously hampered.
The hosts were overwhelming favourites regardless of Malaga's woes but they struggled to breakdown the visiting rearguard in a cagey opening.
Indeed, the best they could muster in the attacking third arrived on 16 minutes when Mario Goetze seized upon a rare defensive lapse and teed up Lewandowski, but the Pole's attempted chip from 25 yards dropped a yard over the crossbar.
There was an air of frustration creeping into Signal Iduna Park and it was replaced by one of disbelief on 25 minutes when the away team surged forward and grabbed the lead.
Isco clipped a pass into Julio Baptista who laid the ball off for Joaquin 25 yards from goal. The Spaniard showed neat feet to outfox Marcel Schmelzer before dispatching a low shot into the bottom corner.
It was a huge goal in the context of the tie and Dortmund struggled to come to terms with it until a moment of brilliance saw them restore parity five minutes before the break.
The lively Goetze cut in from the right and showed good vision to pick out Reus, who sent Lewandowski racing clear with a sublime back heel flick.
The Pole is one of the deadliest finishers in Europe at present and he made it 29 for the season when he rounded Willy Caballero and fired into an empty net to give Juergen Klopp and co a psychological lift.
However, the Spanish outfit almost restored their advantage with the last kick of the half when Joaquin nodded a free header straight at Roman Weidenfeller with the Dortmund defence completely exposed.
The hosts showed a greater sense of urgency in the second period but after Lewandowski threatened straight from the kick off, Malaga came close again.
Duda hung a ball up to the far post for Martin Demichelis who nodded back across goal for Joaquin, but his header was brilliantly saved by Weidenfeller.
Back up the other end and Sergio Sanchez's miscued header fell kindly for Goetze but he thrashed his volley well wide of the near post.
Caballero then threatened to recreate his first-leg heroics with a sensational double save to deny Goetze.
The visitors remained a threat on the break and eight minutes from time they snatched what seemed to be the winning goal when Baptista's cross-shot was turned in by Eliseu, who netted his fourth goal of the competition.
Dortmund looked to be heading out but in the second minute of four added, Reus pounced to turn home a loose ball inside the six yard box after Neven Subotic's cut back was deflected into his path.
And Santana won it just seconds later when he stabbed home in controversial circumstances, as the Brazilian defender looked to be one of four Dortmund players in an offside position before he eventually tapped in the goal that put his side into the last four.
MAN OF THE MATCH
Marco Reus (Borussia Dortmund) - The young attacker endured a frustrating night but took centre stage when it mattered most. He was at the heart of Dortmund's best moves, teeing up Lewandowski and netting an all-important second goal that sparked the sensational comeback.
DORTMUND: Weidenfeller 6, Piszczek 6, Subotic 6, Santana 6, Schmelzer 6, Gundogan 6, Bender 5, Blaszczykowski 5, Gotze 6, Reus 7, Lewandowski 6. Subs: Hummels 5, Sahin 5, Schieber 5.
MALAGA: Caballero 7, Gamez 6, Sanchez 6, Demichelis 6, Antunes 6, Joaquin 7, Toulalan 6, Camacho 6, Duda 6, Isco 6, Baptista 6. Subs: Eliseu 6, Portillo 5. Santa Cruz 5.