The Brazilian opened his Champions League account with three goals as the Liga side secured top spot in devastating fashion, while the visitors bow out with a whimper
The Brazil star had not previously scored in Europe's premier club competition, but was in irrepressible form against the Scottish champions at the Camp Nou on Wednesday.
Barca lost their last Champions League outing at Ajax, but were in no mood to repeat that disappointment as they dismantled Celtic with an irresistible attacking display.
Gerard Pique began the rout after just seven minutes, before Pedro doubled the hosts' advantage five minutes before the interval.
Neymar's first goal came in the 44th minute, and he had completed his treble before the hour-mark with two superb finishes before substitute Cristian Tello added a sixth 18 minutes from time.
Georgios Samaras grabbed a late consolation with a header two minutes before the end, but the hosts were in ominous form as they won the group with consummate ease.
Barca dominated the game from the outset, and were rewarded for their early pressure when Pique broke the deadlock after just seven minutes.
Fraser Forster did well to save Alexis Sanchez's deflected shot with his legs, but the Celtic keeper was powerless to prevent Pique from rifling the rebound into the roof of the net from six yards.
The game continued to be played exclusively in Celtic’s half, but Martino’s men had to wait until five minutes prior to the break to finally double their advantage courtesy of Pedro.
Pique was again heavily involved as he played a fine pass to Neymar, who raced away from Efe Ambrose and squared for the winger to finish neatly from close range.
And Barca extended their lead further just before half-time as Neymar - who was recalled by Gerardo Martino after being rested for the Copa del Rey win at Cartagena - tapped home a typically free-flowing move involving Xavi, Sergi Roberto, Alexis and Martin Montoya.
Xavi and Sergi linked well before the outstanding Sanchez lifted a deft pass into the path of Montoya, who rolled the ball across the face of goal for the Brazilian to convert.
Martino’s side were in no mood to take their foot off the pedal after half-time, and it took Neymar just three minutes of the second period to grab his second of the game following another sumptuous passing move.
The 21-year-old played a slick one-two with Xavi after more good work from Sergi before firing unerringly into the top corner from 10 yards.
And Neymar completed his hat-trick just before the hour as he collected Adriano’s pass down the left, bamboozled Ambrose with some sensational footwork and slotted past Forster, with Matthews unable to clear on the line.
Barca continued searching for more goals to banish the memory of their defeat in Amsterdam, and Tello got in on the act on 72 minutes when his shot deflected past the helpless Forster.
Samaras then restored a semblance of respectability to the scoreline for Celtic on 88 minutes when he headed home a free-kick from close range.