Aduriz pounced on a loose ball to fire Bilbao ahead in the 69th minute at a sun-drenched San Mames and Susaeta curled the ball into the top corner from the edge of the penalty area six minutes later.
It was a morale-boosting victory for Marcelo Bielsa's side, who had struggled to reproduce the sparkling form that took them to the final of both the Europa League and the King's Cup last season and had conceded nine goals in losing their opening two La Liga matches to Real Betis and Atletico Madrid.
Bielsa, a former Argentina coach, and his players have been distracted by the protracted transfer sagas involving Spain pair Javi Martinez and Fernando Llorente.
Martinez, a versatile midfielder who can also play in defence, rescinded his contract at a cost of 40 million euros ($50.42 million) and joined Bundesliga side Bayern Munich last week, while burly striker Llorente failed to find another club and remains with Bilbao for now.
President Josu Urrutia, who tried hard to keep Martinez, now has a large pot of cash to spend on reinforcing the squad, although the club's options are limited by their policy of only signing players of Basque origin.
Bielsa left Llorente, who had been linked in media reports with a possible move to Serie A champions Juventus, out of the squad for the Valladolid game and the club said he had a leg muscle problem.
Several times crosses flew across the face of goal that the towering Llorente thrives on but Aduriz, who joined from Valencia in the close season, and Susaeta were on target to secure Bilbao's first points of the campaign.
Rayo Vallecano, who won their opening two games, drew 0-0 at home to Sevilla in the early kick-off but were lucky to escape with a point after goalkeeper Ruben was dismissed in the 69th minute.
Striker Alvaro Negredo and midfielder Ivan Rakitic both missed penalties for Sevilla, the second of which was awarded when Ruben felled Croat Rakitic in the penalty area and was shown a straight red card.
Negredo's effort in the seventh minute struck a post, while Rakitic's weak shot missed the goal altogether to leave Sevilla coach Michel fuming.
And a stoppage-time winner from Michel secured Levante three points in a thrilling 3-2 home win against Espanyol in which they came back from two goals down to equalise before having Vicente Iborra sent off nine minutes from time.
- Marcelo Bielsa
- Fernando Llorente