In front of a lively crowd, Athletic were on top throughout the entirety of the first half. They got the reward their dominance deserved through Iker Muniain in the 42nd minute, with the winger converting after some slick approach play.
In the second period, the hosts looked the most likely to net again, although couldn't increase their advantage. They thought they had twice, but both Yeray Alvarez and Ander Capa saw brilliant efforts ruled out for offside.
The second semi-final first leg is between Real Sociedad and Mirandes on Thursday. The second leg between those sides will be played on March 4, with Athletic travelling to Granada a day later.
Following their memorable win over Barcelona in the previous round, it was no shock to see San Mames buzzing hours before the match got underway.
The Bilbao Twitter account posted the following clip of some of the scenes from outside the stadium:
With a raucous atmosphere behind them, Athletic started the stronger of the two sides, with Granada backed up and defending for their lives in the early stages.
Inaki Williams was causing a number of problems for the visitors with his searing speed and close control. It was Mikel Vesga who had the first big chance for the Bilbao outfit, though, with his shot blocked by Granada keeper Rui Silva.
Williams was key to Athletic opening the scoring, though. With three minutes to go in the first half, the forward played in a perfect cross and Muniain was on hand to covert from close range.
Per Spanish football writer Rik Sharma, the home side were consistently making inroads down the flanks through Williams:
At half time, OptaJose reflected on a dominant performance from Gaizka Garitano's team:
In the early stages of the second period, Athletic thought they had doubled their lead when Alvarez controlled and finished with aplomb. However, his celebrations were cut short when the assistant referee raised his flag.
Ander Capa then volleyed home for the hosts, prompting more significant celebrations. However, after a lengthy VAR review, it was deemed that Williams was interfering with play in an offside position:
Granada continued to offer little as an attacking threat, with their mindset seemingly geared towards keeping the scoreline down ahead of the second leg.
With the away side sat back, the irrepressible Williams continued to tear forward and he came close to doubling Athletic's advantage when he fired a rasping shot at goal, only to see Silva push it away.
In the latter stages, both teams appeared content with the scoreline, setting up a tense second leg for supporters at Nuevo Estadio de Los Carmenes next month.
Athletic are back at San Mames on Sunday, when they host Osasuna in La Liga. Granada are also at home this weekend, with Real Valladolid the visitors.