Messi, who was at his ruthless best in attack, moves up to 62 goals in the competition, nine short of Real Madrid legend Raul.
The Argentine opened the scoring with a trademark free-kick from 25 yards, the like of which Barcelona fans have become accustomed to over the years.
Ricardo van Rhijn and Lerin Duarte each spurned clear openings for the Dutch champions before Messi cut inside to drill in a second.
Gerard Pique glanced in Neymar’s brilliantly whipped cross for 3-0 and Messi completed his fourth Champions League hat-trick 15 minutes from time with a low drive from the edge of the box.
Ajax’s miserable night was complete when Victor Valdes pulled off a fine penalty save from Kolbeinn Sigthorsson after substitute Serero was fouled by Javier Mascherano.
PRE-MATCH: Quite incredibly, this was the first competitive meeting between the sides. Linked by a certain Dutch legend, this has been dubbed the Cruyff derby. But Cruyff was not in attendance after a spat with Barcelona President Sandro Rosell.
22’ – GOAL! Messi opens the scoring with a beautifully struck free-kick. Bending it around the wall and in off-the-post, Vermeer had no chance.
32’ – AJAX CHANCE: Ajax create their best chance of the half. Bojan picks out right-back Van Rhijn in space on the far side, but Valdes makes an excellent stop from Van Rhijn’s diving header.
55’ – GOAL! Typical Messi goal. He receives the ball from Sergio Busquets and cuts inside Van Rhijn and drills it beyond Vermeer.
56’ – BARCA CHANCE: Almost a hat-trick for Messi, who knees Neymar’s cross at goal in quite unorthodox fashion, but watches it fly just the wrong side of the post.
69’ – GOAL! Pique makes it 3-0, glancing in Neymar’s brilliant delivery from the left with goalkeeper Vermeer in no mans' land.
75’ – GOAL! Messi has his hat-trick. The Argentine waltzes into space 25 yards from goal and drills a low shot beyond Vermeer to move up to 62 Champions League goals, nine short of Raul’s record.
77’ – AJAX PENALTY SAVED: Sigthorsson steps up after Mascherano brought down Serero in the box – but Valdes pulls off a fine save to his right.
Possession: Barcelona 56%, Ajax 44%
Barcelona have ended a winless run in the Champions League games that stretched back four games (two draws, two defeats). It was their worst run of results in the competition since 2001/02.
Ajax have now won only one of their last nine Champions League games (at home vs Manchester City last season).
Can Messi carry Barcelona again this season? With Neymar still adjusting to Spanish and Champions League football, Messi will be expected to be Barca’s talisman again. But how long can he keep producing match winning performances? On this evidence, a long time yet.
Barcelona: Valdes 8, Dani Alves 7, Pique 7, Mascherano 6, Adriano 7, Busquets 7, Fabregas 7, Iniesta 7, Alexis 7, Neymar 8, Messi 9. Subs: Xavi 7, Pedro 6, Bartra 7.
Ajax: Vermeer 6, Van Rhijn 6, Denswil 5, Moisander 5, Blind 5, Poulsen 7, De Jong 6, Duarte 7, Bojan 7, Sigthorsson 6, Boilesen 6. Subs: Serero 7, Van der Hoorn 6, Schone N/A.
MAN OF THE MATCH
Lionel Messi (Barcelona): Who else? On another night, Valdes or Neymar could have received the accolade, but Messi outshone his team-mates again with a brilliant display of finishing. Could quite easily break Raul’s Champions League scoring record this season on this form.
THE MATCH IN A TWEET