With Lionel Messi missing because of a calf problem and Philippe Coutinho left out amid talks with Bayern Munich over a loan move, the reigning champion was found wanting in attack against coach Ernesto Valverde's old club.
Antoine Griezmann and Frenkie de Jong made their league debuts for Barca, but there was little to celebrate as the champion's 2019-2020 season got off to a lacklustre start at San Mames.
The loss of Suarez to a first-half muscle problem only compounded what proved a frustrating outing for the visitors, who twice hit the woodwork before Aduriz's 89th-minute overhead kick secured all three points.
Aduriz had barely been on the field after coming off the bench, and scored with his first touch, and a magical one it was for the 38-year-old veteran, who plans to retire at the end of this campaign.
The goal helped Aduriz match a record held by Messi, scoring in 15 consecutive seasons in Spain's top flight, something only the Argentinean had achieved before today.
Barca's defeat marked the first time since 2008-2009 that the reigning LaLiga champion has lost its opening match of the new season. Back then, Real Madrid lost 2-1 to Deportivo La Coruna.
It was also Athletic's first victory over Barca in their past 12 meetings, although Ernesto Valverde has now lost five of his six LaLiga away games against his previous club.
Inaki Williams started the worries for Barca early on, forcing a superb save from Marc Ter Stegen in the first half after a shot from outside the box, and Barcelona failed to piece together any meaningful attacks throughout the encounter.
Rafinha saw a long-range effort tipped on to the bar in the first half by Unai Simon, and the Brazilian created another chance inside the box with some fancy footwork, but that shot was blocked by a solid defence.
Barcelona had one final chance immediately after Aduriz's moment of magic with a free-kick in stoppage-time, and while Rafinha's delivery was met well by Clement Lenglet, the Frenchman's header was tipped over the bar by Simon, leaving the visitors with nothing to show for their uninspiring efforts.