Gerard Pique got the hosts off to the perfect start when he slammed home from close range after Celtic keeper Fraser Forster had done well to deny Alexis Sanchez.
Neymar then produced a magical piece of skill to ghost past Efe Ambrose to set up Pedro for the second and rounded off a fine team move with the simplest of finishes to make it 3-0 a minute before half-time.
The Brazilian striker then added a brilliant fourth with a curling finish after a one-two with Xavi before completing his hat-trick with an individual effort 10 minutes later.
Cristian Tello made it 6-0 with a deflected strike 18 minutes from time before Giorgious Samaras pulled one back for the Scottish champions.
“I am very happy to score my first three goals in the Champions League, but the most important thing was that the team played well,” he told Spanish TV station Canal Plus.
“We needed to change the dynamic after the recent defeats and now we have to concentrate on La Liga.”
Despite being already assured of a place in the last 16, Barca boss Gerardo Martino sent out the message that he didn’t want a repeat of the lacklustre performance that saw his side beaten 2-1 by Ajax in their last Champions League outing as he named a strong side.
Barca could even have gone in front inside three minutes as only a last-ditch challenge from Virgil Van Dijk prevented Xavi from having a clear sight of goal.
However, the reprieve only last a further four minutes for the visitors as Pique coolly volleyed home his second goal of the season.
Forster had to be alive to deny Pique his second midway through the half as Barca continued to swarm forward with ease.
And the only surprise was that it took until the 39th minute for the La Liga leaders to double their advantage as Neymar skipped past Ambrose on the right side of the area before squaring for Pedro to slot home.
Neymar then scored his first Champions League goal just before the break as a lovely move involving Sanchez, Sergi Roberto and Martin Montoya found the later in behind the Celtic defence and he rolled the ball into Neymar’s path to slot into an unguarded net.
The flurry of goals continued after the restart as Neymar got his second of the evening just three minutes into the second period with a precise finish into the top corner from 20 yards.
And the 21-year-old then embarrassed Ambrose once more as he nutmegged the Nigerian before rolling the ball past a helpless Forster.
Neymar ought to have had his fourth of the night 26 minutes from time when he rounded Forster only for Pedro to take the ball off his teammate and fire the ball of Van Dijk with the whole goal to aim at.
Substitute Tello did add a sixth as his shot from outside the area deflected in off a stary Celtic leg.
However, there was time for Celtic to salvage some pride as Samaras headed home Charlie Mulgrew’s free-kick a minute from time.