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The Blaugrana, who needed a victory to guarantee they progress into the last-16 stage as group winners, were given the ideal start after Gerard Pique struck into the roof of the net after seven minutes.
Neil Lennon's men held strong until the final five minutes of the first half, as Pedro doubled the advantage on the 40-minute mark, before Neymar registered his first Champions League goal on the stroke of half time, tapping home from close range.
The diminutive Brazilian picked up where he left off after the interval, exchanging a neat one-two with Xavi before finding the top corner past goalkeeper Fraser Forster.
Nine minutes later the 21-year-old secured the match ball, finding the bottom corner via a deflection off the boot of Adam Matthews.
Neymar then turned provider to set up Christian Tello, whose effort nestled into the top corner of the goal.
Georgios Samaras bagged a consolation for the Scots in the closing stages, as Barca sealed their place at the summit of Group H in style ahead of the draw for the latter stages.