The north London side were let off by Guillermo Fernandez's missed early penalty but failed to take advantage after the youngster was sent off ten minutes later
Guillermo Fernandez provided all the game's talking points, having his self-earned penalty saved on 23 minutes before being sent off for an elbow as the Basque side held on.
The hosts began the game in encouraging fashion, with Inaki Williams racing through on goal with seconds on the clock only to see his attempt well saved by Reice Charles-Cook.
And the young goalkeeper was to be called into action soon again after Fernandez was felled in the box, but was equal to the Athletic captain's penalty, tipping it around the post.
Things then went from bad to worse for Fernandez, as he was adjudged to have deliberately elbowed Sead Hajrovic on 34 minutes and was sent for an early bath.
Serge Gnabry, who recently featured for the Gunners' first team in the Capital One Cup, was at the heart of the visitors' attempts to carve out a lead.
The 17-year-old was the provider as Martin Angha's drive was well turned away and then saw his own attempt well held.
And, despite a flurry of late attacks from both sides, there was no late breakthrough in front of a 10,000 crowd at the San Mames.