Athletic had plenty of chances and possession but no luck and Espanyol took full advantage with goals from Hector Moreno, Victor Sanchez, Christian Stuani and Joan Verdu.
They also lost Iker Muniain and Ibai Gomez to injury as a three-match unbeaten run ended abruptly.
Athletic were the better team for most of the first half, even if they did end it trailing, and were clearly on top early on.
Markel Susaeta brought a good early save out of Francisco Casilla with a close-range effort, and the goalkeeper was stretched again by Jon Aurtenetxe's header before Oscar De Marcos blazed over.
It was against the run of play that Hector Moreno nodded Espanyol in front with his first goal since last March, rising to meet in Simao Sabrosa's whipped free-kick and heading towards the far post.
The hosts continued to press but Ander Herrera drifted a shot over the bar and then, deep in first-half injury time, Aymeric Laporte fired high when the ball sat up for him following a free-kick into the area.
Marcelo Bielsa may have had some choice words for his squad at the break and they started the second half brightly, but Andoni Iraola sent a good chance over and Casilla then used all of his 6ft 3in frame to pluck Aritz Aduriz's header out of the air.
Athletic then lost a second player to injury with Gomez - himself a first-half replacement for Muniain - limping off, but it was the 53rd minute introduction of Espanyol substitute Victor Alvarez that had the most profound impact on the match.
The visitors looked suddenly revitalised and were quickly on the attack. Sergio Garcia appeared to handle a high ball in the area but there was no whistle and Stuani beat a defender and the goalkeeper to meet Joan Capdevila's deflected cross at the far post, heading narrowly wide.
Moments later, Alvarez set up their second with a delightful chipped ball into the path of Sanchez who prodded it past Gorka Iraizoz, who was trapped in no man's land.
Athletic looked shell-shocked and Espanyol took full advantage to snatch a third just seconds later, Stuani showing great desire again as he raced through the lethargic Athletic defence to turn Alvarez's cross home.
It should have got worse just after the hour mark when Verdu had a legitimate claim for a penalty, brought down by Ander Iturraspe when he checked a run inside the area.
The hosts were feeling thoroughly sorry for themselves, and squandered the few chances they made as Susaeta headed wide with Casilla out of position and Igor Martinez shot straight at the goalkeeper when well placed.
Instead, they were the architects of their own downfall once more with a horrible challenge from Iraola on Alvarez earning him a booking and Espanyol a penalty, which Verdu initially saw saved by Iraizoz before prodding home the rebound.
Nothing would go for Athletic, with Susaeta finding the net in the 89th minute only to be flagged offside.