Bilbao bow out of King's Cup
Spain striker Fernando Llorente gave the Basque club hope with a goal in the 42nd minute of the last-32 clash at the San Mames.
But a superb volley from Juan Jose Collantes in the 72nd minute and a freekick from Edu Albacar six minutes later put the tie well beyond their reach.
Getafe, losing finalists in 2007 and 2008, advanced to the last 16 with a 3-1 aggregate win over la Liga rivals Espanyol.
The Madrid-based club were leading 2-0 from the first leg at home and a 1-1 draw in Barcelona in the return match was enough to see them through against the 2006 winners.
Striker Roberto Soldado put Getafe ahead when he outpaced the Espanyol defence after a long clearance from goalkeeper Jordi Codina and finished coolly past Cristian Alvarez.
Uruguay forward Ivan Alonso equalised in the 37th minute when he smashed in the rebound after Codina had saved his header from a Shunsuke Nakamura cross but Espanyol were unable to breach the Getafe defences again.
In other matches, Racing Santander reversed a 1-0 first-leg deficit to second-division Salamanca to win 4-1 on the night and 4-2 on aggregate.
Real Mallorca lost the first leg at la Liga rivals Real Valladolid 2-1 but won 1-0 at home on Wednesday to advance on the away goals rule.