The Catalan outfit have now joined Las Palmas and Real Madrid on maximum points from their opening two fixtures, while Bilbao remain in the relegation zone having lost both of their league games at the start of the 2016-17 campaign.
Barcelona came close to making the breakthrough inside four minutes when Lionel Messi volleyed a pass into the path of Denis Suarez, who curled one towards the top corner, but the summer signing's effort just missed the post.
Bilbao's first shot on target came in the 12th minute when Marc-Andre ter Stegen presented the ball straight to Benat just outside the Barcelona box, but the new number one was able to prevent his own blushes with a smart save.
The home side grew in confidence as the first period developed, but it was Barcelona that made the breakthrough in the 21st minute of action when Rakitic headed a Turan cross into the corner from inside the box.
Bilbao continued to enjoy good moments in the final third, however, as pacy attacker Inaki Williams looked to get at Samuel Umtiti, who picked up an early yellow card for handball and looked capable of making another mistake.
Denis Suarez, Umtiti and Messi all had half-chances to double Barcelona's lead in the latter stages of the first period, while Aritz Aduriz and Benat both tested Ter Stegen with strikes from distance as both teams threatened to register the game's second goal.
Turan had the best opportunity of the lot in the final minute of the first period when a devastating Barcelona counter saw Messi feed the Turkish international in space, but the attacker somehow placed his effort wide of the near post.
Aymeric Laporte had the first half-chance of the second period when he met a dangerous corner from Benat, but the centre-back missed the target under pressure from his own teammate Aduriz, who was also looking to make contact.
Barcelona came close to a second in the 54th minute when Luis Suarez found Messi and the Argentine curled one towards the bottom corner, but the ball flashed wide of the post during an end-to-end period of the match at San Mames.
Luis Suarez then sent a rasping volley just wide of the far post, before Raul Garcia came close with an attempt down the other end as Bilbao started to force the issue approaching the final 25 minutes of action.
Messi had another golden chance in the 70th minute when Luis Suarez found the Argentine once again, but he fired over the crossbar from inside the box as Bilbao survived yet another dangerous moment.
Benat had Bilbao's best opportunity to level in the latter stages when he bent a brilliant free kick towards the top corner, but the midfielder's effort missed the post as Barcelona secured all the points at San Mames.
Luis Suarez had a wonderful chance to score a second for the visitors in second-half stoppage time, but after being set up by Messi, the striker had his effort cleared off the line by Eneko Boveda.
Next up for Barcelona is a home match against Deportivo Alaves after the international break on September 10, while Bilbao will attempt to put their first points on the board when they travel to Deportivo La Coruna on September 11.