The Brazil international scored two late goals after coming on as a second-half substitute to prevent his team from dropping points, after a profligate display.
Luis Enrique's side enjoyed long spells of unrelenting pressure and produced some fine football, but Barca almost put itself in a difficult situation after 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 hardly troubled Claudio Bravo at the other end and they rarely 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.
However, the introduction of Neymar from the bench provided a much needed spark in attack and he broke the deadlock 12 minutes from the end.
The Brazil international wrapped up the win a few moments later to secure a comfortable triumph, consigning Athletic to an 11th successive league defeat at Camp Nou.
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.
Benat forced Bravo into action with less than two minutes played, as the former Real Betis star found space in the left side of the area and shot across goal.
It did not take long for Barca to wake up, though.
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.
Fresh from making his Spain debut on Monday, Munir puzzled the Athletic defense with a jinking run and, after creating space for himself, the 19-year-old blazed over from the edge of the area.
Barcelona unsurprisingly dominated possession in the first half and carved through Athletic at will.
They were kept at bay by some desperate defending just before the break, though, as Aymeric Laporte produced a fine block to halt a Lionel Messi shot and then Iraizoz denied Munir from point-blank range.
Barca began the second half with similar fervor and gave the Athletic backline numerous difficulties.
Munir saw a 50th-minute effort chalked off 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 Brazilian darted into space left by Oscar De Marcos and coolly slotted under Iraizoz to give Barca a deserved lead 12 minutes from the end.
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.