In a must-win game for the hosts, the Gunners got off to the perfect start with Jon Toral heading home from close range to make it 1-0 after seven minutes.
Athletic struck back almost immediately from the penalty spot through Ager Aqueche, who calmly slotted into the bottom corner.
Both sides dealt with the hard pitch well, playing some excellent, free-flowing football but the score remained 1-1 at the interval.
Quickfire second-half goals from Zak Ansah, Isaac Hayden and John Toral put Arsenal into a commanding lead after 80 minutes.
Arsenal controlled the tempo and dictated throughout the second half but a lack of concentration in the last minute of the game meant Athletic grabbed a consolation goal late to make it 4-2.
Athletic Club remain in second place in Group Six with a game left to play against Olympiacos next week. Should they avoid defeat against the Greek side they will advance through to the last 16 of the tournament as group winners.