Victory for Barca saw them progress into the last 16 as winners of Group H, while Neil Lennon's Bhoys were destined to see their continental campaign come to a close on Wednesday night.
It took just seven minutes for the hosts to break the deadlock in Catalunya, with some sloppy defending from Celtic allowing Alexis to spring into life, force a save from the boot of Fraser Forster and see Gerard Pique follow up to poke into the roof of the net.
Barca doubled their lead on 39 minutes when Neymar squared for Pedro to crash home, and the Brazilian forward got in the act himself just before the interval when Martin Montoya teed up his first goal in European competition.
His second arrived three minutes after the re-start, with a neat interchange with Xavi on the edge of the box allowing him to fire into the top corner on the slide, and he completed his treble 10 minutes later after brushing past Efe Ambrose and forcing the ball over the line despite the best efforts of Adam Matthews.
Substitute Cristian Tello grabbed a sixth on 72 minutes, with his effort from the edge of the box taking a wicked deflection off Virgil van Dijk to leave Fraser Forster wrong-footed, before Georgios Samaras snatched a late consolation for Celtic as he nodded in a Charlie Mulgrew free-kick.
As expected the home side dominated possession from the start, with Joe Ledley and Matthews both putting Celtic under pressure with some slack passing.
In the fifth minute a timely Van Dijk tackle prevented Neymar's shot from 12 yards testing Forster, although the goal was only seconds away when the Hoops defence was exposed again.
Alexis Sanchez's low drive was deflected by Efe Ambrose on to Forster's legs but Pique was in the right place four yards out to knock the ball into the net.
Thereafter, Barca's dominance was at times mesmeric as they moved the Celtic players around the pitch with ease.
In the 26th minute Pique almost got a second when Xavi's deep free-kick from the right arrived at the back post but his shot from five yards was blocked by the foot of Ambrose.
At times the home side, inspired by the wonderful talent of Alexis, were guilty of over-playing but in the 40th minute Neymar skipped past Ambrose inside the box and cut the ball back for Pedro to steer it low past Forster from six yards.
Things went from bad to worse for Celtic.
On the stroke of half-time Alexis cleverly dinked the ball over the Celtic defence for right-back Montoya to set Neymar up for an easy third.
Mulgrew replaced Teemu Pukki for the start of the second half but within two minutes Neymar played a one-two with Xavi and slammed the ball high into the net from 16 yards before Van Dijk could intervene.
The Parkhead side were heading for a thrashing and they could do little about it.
Neymar got his hat-trick in the 58th minute when he took a pass from Adriano, put the ball through the legs of Ambrose and slipped the ball past Forster with Matthews unable to clear.
The Brazilian should have made it six when he evaded the Hoops defence with time and space to go round Forster but Pedro took the ball off his toes and blasted a shot off Van Dijk and over the bar.
Still Barca drove forward, relentlessly.
Tello had replaced Alexis and when his shot came off Van Dijk and wrong-footed Forster for the sixth, Celtic looked on the verge of total capitulation and only a block from Forster moments later denied Neymar another goal.
A bedraggled Celtic side - and their small band of supporters high up in the Nou Camp stands - had little consolation when Samaras headed in a Mulgrew free-kick in the 89th minute and he might have grabbed a second moments later, but by then it was far too little too late.