It was the visitors' heaviest defeat in Europe since they lost 5-0 away to Artmedia in 2005 and in truth it could have been more damaging.
The Hoops, with three points from their first five fixtures, were guaranteed to finish bottom of Group H before the trip to Catalonia and they found themselves behind after only seven minutes when Barca defender Gerard Pique opened the scoring from close range.
Barcelona, who needed a point to finish top of the section, were in scintillating form and when Pedro Rodriguez and Neymar added a second and third before the break a thrashing was on the cards.
Neymar scored his second two minutes after the break before grabbing his hat-trick before the hour mark as the Hoops all but crumbled.
Substitute Cristian Tello got in on the act in the 71st minute when his drive was heavily deflected past Fraser Forster by Parkhead defender Virgil van Dijk for number six before Georgios Samaras grabbed a late goal.