Athletic Bilbao ended Atletico Madrid's 28-game unbeaten run at home to take a narrow lead into their Copa del Rey semi-final second leg.
The visitors clung on after Alejandro Berenguer's first-half penalty, given for Reinildo Mandava's wild lunge.
Atletico were awarded a stoppage-time spot-kick for a foul on Alvaro Morata but it was ruled out when the Spain striker was shown to be offside.
Morata also put a header wide with the final touch in a dramatic finale.
Athletic, who have not won the Copa del Rey since 1984, could have gone two up in the second half but Jan Oblak saved Unai Gomez's long-range shot and Asier Villalibre wastefully put the rebound into the side-netting.
Their defender Dani Vivian also had to clear off the line from Angel Correa to preserve the Basque club's slender advantage.
Atletico's unbeaten run at home stretched back more than a year to January 2023 - a 1-0 defeat by Barcelona in La Liga.
The second legs will be played on 27 and 29 February.