The Brazilian forward had never scored a goal in the elite competition before tonight and his goals as well as strikes from Gerard Pique, Pedro and Cristian Tello ensured Barcelona topped Group H.
The hosts took the lead after only seven minutes when Pique poked the ball home after latching onto Fraser Forster's save from an Alexis Sanchez shot.
Barcelona grabbed their second goal six minutes before the half-time whistle when Pedro slid the ball home from close range.
And on the stroke of half-time, Barcelona sealed the match with a fantastic team goal which saw Neymar tap-in from five yards.
Neymar grabbed his brace two minutes after the restart with a fine individual effort, wrapping the ball around Forster to find the top corner of the net. And on 58 minutes, he had his third, sliding the ball past a helpless Forster after beating Ambrose.
Just three minutes later substitute Tello made it six when he picked up Adriano’s pass on the edge of the box before firing into the goal courtesy of a wicked Virgil van Dijk deflection.
7’ - GOAL: Pique has scored for Barcelona! Alexis shot is well saved by Forster but the ball rebounds to the defender who prods home to make it 1-0.
39’ – GOAL: 2-0 Neymar sells his marker a wonderful dummy before squaring the ball to an unmarked Pedro to slide the ball into the back of the net.
45’ - GOAL: Neymar finally has a Champions League goal! He completes a fantastic team goal to tap in from Montoya's squared ball.
47’ - GOAL: 4-0 And Neymar has his second of the match. He finds the top corner of the net after some wonderful one-touch football from the Brazilian and Xavi on the edge of the area.
58’ - GOAL: Hat-trick hero - Neymar seals a fine display with a wonderful treble. He beats Ambrose with some terrific quick feet before sliding the ball past Forster, and despite Matthews best efforts of clearing the ball, he is unable to prevent the goal.
72’ - GOAL: It's six! Adriano picks out Tello in the centre of the park who shoots and his effort is wickedly deflected and into the net.
88’ - GOAL: 6-1 Celtic have finally got a goal back. Mulgrew's wonderful free-kick is met by Samaras who heads the ball home.
Barcelona have won only three of their last nine European games between this and last season, losing and drawing also three.
The Blaugrana have now won five of their last six games in European competition against Celtic.
Xavi made his 159th European appearance, surpassing Raúl as Spanish record holder. He is now third in the all-time list: P.Maldini (168) and C.Seedorf (161).
Who needs Lionel Messi? Neymar finally broke his Champions League goal drought with a spectacular hat-trick. It may have only been Celtic, but if the Spanish giants continue to play like this they will be very difficult to stop.
MAN OF THE MATCH
Neymar (Barcelona): Who else? The Brazilian forward was absolutely unplayable tonight and he could have had added to his three goals. Not only did he score a hat-trick he was also provider for Barcelona’s second goal.
Barcelona: Pinto 6, Montoy 8, Piqué 8, Mascherano 6, Adriano 7, Sergio 7, Xavi 8, Sergi Roberto 7, Pedro 8, Alexis 8, Neymar 9. Substitutes: Tello 7, Song 6, Dongou 6,
Celtic: Forster 6, Lustig 5, Ambrose 5, Van Dijk 5, Ledley 5, Matthews 5, Brown 5, Biton 5, Boerrigter 5, Samaras 7, Pukki 5. Substitutes: Stokes 5, Commons 7, Mulgrew 7.
MATCH IN A TWEET