The visitors were dealt a blow after 20 minutes when Lionel Messi had to be withdrawn with a hamstring problem, but it did little to disrupt Gerardo Martino's side, who went into the break two goals to the good.
Neymar claimed the first 10 minutes before the interval, tapping home after being set up by Cesc Fabregas, before Pedro ran from his own half to finish in fine style a minute later.
Fabregas found the net with a simple finish on 63 minutes, before netting his second 11 minutes from time with a header from Dani Alves' cross.
Alves then brought down Javier Matilla inside the box in stoppage time, Jorge Molina sending Victor Valdes the wrong way from the spot to spoil the leaders' clean sheet.
That result for Barcelona put daylight between themselves and Atletico Madrid, who dropped points for only the second time this season when they were held 1-1 at fourth-placed Villarreal.
Diego Simeone's side got off to a dream start when Mario Gaspar put through his own net in the third minute, but the hosts replied through another own goal, Juanfran deflecting the ball into his own net with 11 minutes remaining.
It brought to an end Atletico's run of three consecutive victories as they lost ground on the leaders.
Valencia's troubled start to the season continued as they twice had to come from behind to earn a 2-2 at home with struggling Real Valladolid.
Javi Guerra put the visitors in front in the ninth minute, Dorlan Pabon equalising 20 minutes later.
Gilberto Garcia put Valladolid ahead for a second time five minutes after the break, but substitute Sofiane Feghouli ensured the points were shared with his 76th-minute equaliser.
Elsewhere, Sevilla bounced back from two consecutive defeats with a 3-1 win away at 10-man Espanyol.
Federico Fazio put the visitors ahead as early as the third minute, wih Vitolo doubling the advantage seven minutes later.
Sergio Garcia pulled a goal back for the hosts midway through the first half, but Carlos Bacca made the game safe for Sevilla with a goal in the 59th minute.
Espanyol, who are now winless in four matches, saw Victor Sanchez dismissed for a second bookable offence five minutes before the end as Sevilla climbed above their opponents in the table.
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