Zak Angah and Isaac Hayden were also on target for the hosts as they claimed the three points they needed against the Spanish outfit who faded in the second half
The Gunners took the lead through Jon Toral early on but were pegged back by the visitors who impressed in the first half. However, the second period was a different story and a rampant Arsenal put three past Athletic before they could reply.
Terry Burton's starting line-up included the highly-rated trio Chuba Akpom, Thomas Eisfield and Zak Angah, all of whom have already threatened to break into Arsene Wenger's squad this season. While the visitors went for the same line-up which put five past Marseille in their last outing.
Arsenal's first opening of the game fell to Olsson in the opening 10 minutes, but his right-footed shot was tipped over the bar by an alert Arrizabalaga. However, the Gunners took the lead from the resulting corner as Toral rose highest to head home.
The visitors almost registered an instant reply but Reice Charles-Cook got down well to deny Mikel Santamaria a certain goal after a rapid Athletic counterattack.
The Basque outfit were not to be denied for long though, as Arsenal's Isaac Hayden was adjudged to have brought down Santamaria in the box in the 12th minute. Ager Aqueche stepped up and converted the spot kick with aplomb to bring the Spaniards back on level terms.
A fine move from the Gunners after 20 minutes ended with Ansah firing over the bar from the edge of the area, after Eisfield had brilliant nodded Angha's diagonal pass into the forward's path. Moments later the hosts thought they had taken the lead when Ansah slotted past the keeper after he was threaded through by Olsson, but the offside flag came to the visitors' rescue.
The momentum swung towards the visitors after the on the half-hour with Burton's side having Charles-Cook to thank for keeping them level with a string of fine saves.
Arsenal were significantly better after the break and were inches away from going ahead when Akpom came a whisker away from turning in Hayden's cross from the right flank.
Just as the hosts were beginning to strut their stuff, they were given a reminder of the visiting teams quality, Santamaria brought the best out of Charles-Cook to deny him his second from close range.
It proved to be a vital save as Arsenal went straight up the other end and got their noses in front. Angah provided the finish from close range after a superb combination between Toral and Hayden on the left-hand side.
Two soon became three as the Gunners began to put their opponents to the sword. Toral bagged his second of the match by heading in Angha's cross-cum-shot after more impressive build-up play from Olsson.
The Bilbao players' heads dropped after the third and it wasn't long before the rampant hosts added another. Hayden got himself on the scoresheet by prodding the ball into the net from close range following a scramble in the area.
The Spaniards did rally late on and grabbed a deserved consolation when Yerai Alavarez headed home after some slack defending from Arsenal.