King's Cup holders Barcelona beat Real Sociedad 1-0 in their quarter-final first leg to end a nine-and-a-half year barren spell at home of the Basque side while Atletico Madrid crushed Eibar on Thursday.
Brazil forward Neymar won and scored a penalty in the 21st minute after being tripped by Aritz Elustondo to decide the game but spurned two clear chances after the break that would have given Barca a more comfortable lead in the tie.
Sociedad had not lost to Barcelona at their Anoeta home in any competition since 2007 and could have struck an early blow when Willian Jose went down in the box in the first minute after a challenge from Gerard Pique but was denied a penalty.
Spain defender Pique made a vital block later in the first half to prevent Asier Illarramendi levelling from the edge of the box after a lay off from Carlos Vela.
Teenager Mikel Oyarzabal, scorer of the only goal in a Sociedad victory over Barca last April, came closest for the home side, firing just wide of the far post in a sweeping breakaway move midway through the second half.
"We had to work very hard for this result. The win gives us a lot of belief because it's such a difficult stadium for us but seeing how Real Sociedad play we know it's still going to be complicated," Barca coach Luis Enrique told reporters.
"We focused very hard to stop their transitions and limit their high pressing game. This is the first step to the semi finals but 1-0 is still a result which gives the opponent a chance."
The second leg at the Nou Camp takes place next Thursday.
Earlier, Atletico Madrid put one foot in the semi-finals as they eased to a 3-0 win over Eibar, thanks to goals from Antoine Griezmann, Angel Correa and Kevin Gameiro.
Griezmann headed Atletico in front in the 28th minute and Argentine winger Correa doubled their advantage on the hour by sweeping the ball home after a run by Yannick Carrasco, netting Atletico's 500th goal under coach Diego Simeone.
Substitute Gameiro stretched Atletico's lead by heading in from close range in the 67th after replacing Correa to give Eibar little chance of turning the tie around in the second leg at their Ipurua stadium next Thursday.
"The victory makes me very happy, the team gave the right response in an important game," Simeone said.
Real Madridlost 2-1 at home to Celta Vigo in their first-leg on Wednesday while Alaves beat second division Alcorcon 2-0.