Although Athletic led through Fernando Llorente's 20th minute goal, Raul immediately levelled for Schalke and after the Spaniard netted his second, the Germans looked good to add further goals.
But Llorente headed in another 17 minutes from time and, after Oscar De Marcos put them ahead to silence the crowd, Iker Muniain scored a fine fourth with the last kick of the game.
Athletic arrived in Germany in dismal form since their impressive elimination of Manchester United in the previous round, having lost two and drawn one in La Liga since.
Schalke sniffed blood and dominated possession in the early stages, only for poor finishing to cost them a chance of making it pay as Klaas Jan Huntelaar and Jefferson Farfan missed the target.
Instead, it was Athletic who snatched the lead almost out of nothing in 20th minute.
De Marcos crossed from the right for Markel Susaeta to fire off a relatively tame shot, but Timo Hildebrand spilt it horribly and Llorente prodded home at the second attempt.
However, Schalke needed just 31 seconds to level, with Raul turning in Atsuto Uchida's cross at the near post.
Farfan's fizzing shot was turned away, Raul fluffed a simple chance and Kyriakos Papadopoulos headed over as the missed chances piled up for the hosts.
But Raul was lucky to avoid a booking for what appeared an obvious dive in the area towards the end of the half.
Schalke substituted the injured Hildebrand at the interval, sending on the little known Mathias Schober, who had been elevated from fourth choice by injuries.
Athletic piled on pressure early in the half looking for ways to test the new man, but it was Schalke who had the ball in the net in the 51st minute, only to see Huntelaar flagged offside as he poked home.
The next one did count a minute shy of the hour mark when the ball sat up and Raul lashed a looping volley beyond the reach of Iraizoz.
They kept pushing, and Christian Fuchs' powerful shot troubled Iraizoz before the ball then came out to Raul who saw his cheeky chip across goal go just wide.
Just when it began to seem like a question of when, not if, Schalke would score again, Athletic claimed a stunning equaliser as Llorente met Ibai Gomez's corner at the near post.
They were ahead in the 81st minute when Schober could not hold Muniain's shot and De Marcos rolled home the rebound.
Schalke's night got no better, as Huntelaar's late long-range shot crashed back off the upright and Iraizoz denied Raul from close range, but there was worse to come as Athletic broke and Inigo Perez squared for Muniain to fire into the top corner and give the Spaniards an imposing advantage.