Athletic Club's UEFA Europa League adventure will continue into the semi-finals and a tie with Sporting Clube de Portugal after FC Schalke 04 became the latest high-profile side to fall victim to Marcelo Bielsa's Lions.
Chasing a 4-2 first-leg deficit, the visitors reduced the arrears though Klaas-Jan Huntelaar's tenth goal of the tournament this season just before the half-hour. The hosts responded with a stunning Ibai Gómez strike before the returning Raúl Gonzaléz, and Markel Susaeta, exchanged goals within three minutes of each other after the restart.
Victors against Manchester United FC in the last round, fans of the Leones packed San Mamés hoping to see more of the high-tempo, pressing style they have become accustomed to. It was the visitors who set the pace in the early stages, however, with Huntelaar denied a scoring chance from close range by the alert Jon Aurtenetxe.
At the other end, Iker Muniain headed harmlessly at goalkeeper Lars Unnerstall but it was the 1997 UEFA Cup champions who continued to look the more likely scorers. Huntelaar did so with a low drive from the edge of the area that was touched in by goalkeeper Gorka Iraizoz.
Seeking the inspiration to get going, Athletic found it four minutes before the break through substitute Gómez – on for the injured Ander Herrera – who unleashed a spectacular shot from distance on the left that flew past Unnerstall. It was a memorable way for the 22-year-old to open his senior account.
Undeterred, Huub Stevens' side persevered and were in front again seven minutes after the break when Raúl capitalised on some neat build-up play by Huntelaar and Chinedu Obasi before shooting in off an upright.
Determined to extend a seven-match unbeaten home run in European competition, Athletic rallied and were on terms again when Susaeta struck the ball in low at the near post following Muniain's assist. A last-four encounter against Portugal's Lions, Sporting, awaits the Basque side, with the first leg at the Estádio José Alvalade on 19 April.