Rakitic finished off an excellent team move after 20 minutes, but with Lionel Messi and Luis Suarez uncharacteristically wayward in front of goal, Athletic nearly grabbed a point when Benat Etxebarria's free-kick flew just wide late on.
Barca join Real Madrid and top-of-the-table Las Palmas as the only sides with two wins from their first two games. Champions League finalists Atletico Madrid are already four points off the pace after disappointing draws against newly-promoted Alaves and Leganes.
"It is very intense, there is a lot of pressing. Both teams played well, but in the end we deserved the win."
Still without Neymar due to his exertions in winning Olympic gold and the injured Andres Iniesta, Barca demonstrated their greater strength in depth this season as new recruits Denis Suarez and Samuel Umtiti shone, while Arda Turan proved an able deputy for Neymar alongside Messi and Suarez.
"In terms of tempo it was a frenetic game, not usually the kind you get at this stage of the season," said Barca boss Luis Enrique.
The return of Marc-Andre ter Stegen in goal in place of the departed Claudio Bravo was Barca coach Luis Enrique's only change from the opening day 6-2 thrashing of Real Betis.
Ter Stegen was featuring in La Liga for just the eighth time in his third season with the Catalan giants as Bravo had been first choice in the league for the past two seasons.
And the German's notorious desire to play out from the back nearly cost Barca the opener on 12 minutes when he gifted the ball to Benat, but made amends by repelling the midfielder's fierce effort with his face.
The champions failed to take advantage of a series of chances to extend their lead either side of the break as Gorka Iraizoz turned Messi's header to safety before Turan shot into the side-netting with a furious Suarez waiting for a cross in the middle.
Athletic's attacking threat increased after the
introduction of Raul Garcia as the former Atletico Madrid midfielder fired inches wide before Inaki Williams's effort moments later was placed too close to Ter Stegen.
And only a sensational goal-line clearance from Eneko Boveda denied Suarez his goal with the last kick of the game.
Despite their perfect starts to the campaign, Madrid and Barca trail Las Palmas at the top of the table after the Canary Islanders smashed Granada 5-1 with new signing Kevin-Prince Boateng again on target.
Boateng also netted in a 4-2 win at Valencia last Monday and displayed a t-shirt honouring the nearly 300 victims of an earthquake in central Italy this week after scoring having spent three years at AC Milan.
Sevilla failed to match their thrilling 6-4 win over Espanyol last weekend but picked up a valuable point in a 0-0 draw at Villarreal.
Alaves remain unbeaten after a 0-0 stalemate with Sporting Gijon.
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