The two sides were level heading into the final 11 minutes of action before substitute Neymar made all the difference.
The Brazilian struck a late brace to help the Catalan outfit maintain their 100% start to the new La Liga season.
Here, Sports Mole dissects the 90 minutes of football between the two Spanish rivals.
On target: 8
On target: 2
Was the result fair?
Bilbao frustrated the home side for long spells this afternoon, but there was only ever one team that looked capable of picking up all three points. Bilbao had their moments, especially on the counter-attack, but the fact that they managed just three attempts during the 90 minutes is an indication of their struggles in the final third. Barcelona might have put the game to bed at an earlier stage after creating a number of opportunities, but teenage sensation Munir El-Haddadi was guilty of missing four or five good chances. The fact that the Catalan outfit eventually made the breakthrough was not a surprise, with Bilbao simply unable to deal with the quality from the Barcelona bench. It is not a disastrous result for Bilbao, but they have now lost two of their first three league games of the new season.
The signs are extremely positive for Barcelona, even at this early stage of the season. Luis Suarez is still to come into this XI, while Neymar - who ultimately proved the match-winner - did not start as the Brazilian continues to work his way back to fitness. The Catalan outfit have such quality all over the pitch and had too much for the Basque side this afternoon. It was a game of patience, especially in the first period as they dominated much of the ball, but missed opportunities cost them the chance to take control at an earlier stage of proceedings. In truth, Bilbao did not cause too many problems in the final third, with Jeremy Mathieu continuing his impressive start to the season with a solid display. Ivan Rakitic was also brilliant in the middle of the park, with the Croatian controlling the tempo. Bilbao will worry plenty of teams this season in both the Champions League and La Liga, but Barcelona were in complete control at the Camp Nou.
It has been a physically-demanding start to the season for Bilbao, who had to overcome Napoli in a two-legged affair to book their spot in the group stages of the Champions League. They started the La Liga season with a 1-0 defeat at Malaga, but did pick up three points against Levante before the international break. For long spells it appeared that they would claim an unlikely point at the Camp Nou, but they could not make it through the final 10 minutes. It was not all doom and gloom, with Iker Muniain and Ander Iturraspe both having chances for the away side, but they always offered the impression that they were playing for a goalless draw, even in the first period. Whether Bilbao can secure another top-four finish this season will depend on their home form - which was excellent last season - but they will need to pick up the odd point against the top three and indeed the teams around them on the road.
Sports Mole's man of the match
Neymar: The Brazilian is still working his way back from that horrific back injury that he suffered at the World Cup, but he looked in full flow this afternoon after entering as a second-half substitute. His introduction came at a time when Bilbao were tiring and the former Santos attacker took full advantage. Both of his goals were superb finishes, but Lionel Messi must be credited for providing both assists. When Suarez is back from suspension, not many teams will fancy facing that particular attacking trio.
Messi was again excellent this afternoon, but the Argentine missed a glorious chance to send Barcelona into the lead after 71 minutes. Neymar had beaten two defenders before rolling a low cross into his teammate, but Messi somehow fired his effort high and wide from barely five yards out. It mattered little in terms of the final result, but it was a chance that the attacker would have scored 99 times out of 100.
David Fernandez had a fairly routine afternoon at the Camp Nou. There were a number of fiesty challenges throughout the contest, but the Spaniard issued just the two yellow cards - one for Bilbao's Aritz Aduriz and one for Barcelona's Sergio Busquets. The fact that the contest was such an end-to-end and entertaining affair was partly down to the referee, who was always willing to let the play flow in the correct areas. Both sides had a couple of penalty shouts, but none were strong enough to deserve a spot kick. Overall, a solid display from Fernandez.
Barcelona: The Catalan outfit open their Champions League campaign with a group match against APOEL on Wednesday, before travelling to Levante in the league next Sunday.
Bilbao: Bilbao are also in Champions League action on Wednesday - hosting Shakhtar Donetsk, before the Basque side return to La Liga action at home to Granada next Sunday.