The 21-year-old Brazil international has scored his first hat-trick with Barcelona in Europe and with this huge win The Blaugrana are now sit in the top spot of Group H.
Barcelona finishes this game with 13 points, four points ahead of second-spot Italian club, AC Milan.
Celtic have lost all their group games except only one win over Ajax.
Barca manager Gerardo Martino was happy with the striker performance and admitted that this is the most complete performance of his team in four months and he believes his side is strong in attacking position as well.
Neymar has scored 8 goals in 21 league appearances for Barcelona in this season so far.
The next game of Barcelona will be in La Liga clash against Villarreal at Camp Nou on 14-December, 19:00 GMT.