Luis Enrique's side enjoyed long spells of unrelenting pressure and produced some fine football, but Barca almost put themselves in a difficult situation by spurning a host of chances.
Athletic goalkeeper Gorka Iraizoz proved a difficult obstacle, denying Munir El Haddadi on several occasions and thwarting Pedro early on.
The visitors rarely troubled Claudio Bravo at the other end and they never looked like picking up a first La Liga win at Camp Nou since November 2001.
Barca's woes in front of goal continued early in the second period.
Athletic coach Ernesto Valverde suggested in the build-up that his side's only hope at Camp Nou would rest upon making their hosts "uncomfortable" and his players responded well to the rallying call.
The hosts produced a fine free-flowing move down the right in the fifth minute and, after Martin Montoya's cut-back, Pedro fired a first-time effort straight at Iraizoz.
Barca's superiority continued to grow and Munir should have done better with 19 minutes on the clock.
Barca began the second half with similar fervour and gave the Athletic backline numerous difficulties. Munir saw a 50th-minute effort wiped out for being offside, but Luis Enrique's men continued to pile on the pressure and Iraizoz kept Athletic in the game twice more before the hour mark.
Iraizoz first got down to parry Jordi Alba's low effort away and then, with 59 minutes played, Munir saw his header easily stopped after a clever cross from the left-back.
Barca's wastefulness continued into the final half hour, but Neymar's arrival proved a masterstoke from Luis Enrique.
The victory was wrapped up five minutes later as Neymar benefitted from Messi's excellent run down the right, before placing an effort into the bottom right.
