Borussia Dortmund scored twice in injury time to seal a dramatic 3-2 quarter-final, second-leg win at home to Malaga on Tuesday to reach the last four of the Champions League.
Santana was the 11th-hour hero when he stabbed the ball over the line after a desperate scramble in the final minute.
Real Madrid also reached the semi-finals for the third straight year after Cristiano Ronaldo scored twice in a 3-2 loss to Galatasaray, going through 5-3 on aggregate.
But it was the game in Dortmund that provided the most drama, particularly for the 66,000 crowd gathered inside Signal Iduna Park.
"If we play like tonight we won't win the Champions League, but we have reached our target of the semi-final"
Dortmund manager Jurgen Kloop
With Malaga leading 2-1 in the dying stages, Dortmund's Marco Reus gave his side a glimmer of hope with a 91st-minute equaliser, but the German team needed another because of the away goal rule.
In the frantic closing seconds, Reus managed to stab the ball across the Malaga goal for Brazilian centre-back Santana to toe the ball over the line for the crucial third Dortmund goal to put the Germans through in front of their delirious home fans.
Dortmund's 3-2 aggregate victory came after last Wednesday's first leg finished goalless, and the competition underdogs are into the semi-finals for the first time since 1998.
"There is one very disappointed team in this moment and one lucky team," Dormund manager Juergen Kloop told British Sky television.
"It's unbelievable. It was our worst game in the Champions League this season and not our best football.
"If we play like tonight we won't win the Champions League, but we have reached our target of the semi-final."
Malaga winger Joaquin had given the Spaniards an early away goal before Poland striker Robert Lewandowski's equaliser made it 1-1 at the break.
Second-half substitute Eliseu then looked to have put Malaga in the semis in their debut season in Europe's top club competiton with a goal eight minutes from time, before Dortmund produced two goals in two magical minutes.
It was heart-break for Manuel Pellegrini's side after the Malaga coach had to make a round-trip to his native Chile following the death of his father in the days before the game.
Dortmund continue their run as the only unbeaten team in the competition. But the manner of their latest victory will take some beating.
In the other semi-final, Real Madrid advanced 5-3 on aggregate but only after conceding three goals in a 16-minute span to raise Galatasaray's hope of pulling off what would have been an epic comeback.
Ronaldo appeared to have eased Madrid into the next round with his eighth-minute opener. And the Portugal forward scored again in stoppage time, but not before Galatasaray came alive with Emmanuel Eboue's 57th-minute leveller.
Galatasaray forward Wesley Sneijder scored in the 71st before Didier Drogba adding another goal a minute later.
"It is our own fault it became complicated," Ronaldo told Spanish TV station TVE.
"In football you cannot gift anything. Today that is what happened and it ought to serve as an example for the future to play for 90 minutes."