Messi took his tally to 62 Champions League goals and became the first player to score more than four Champions League hat-tricks, whilst also netting his 24th such treble for Barca.
A day after Cristiano Ronaldo hit three in Real Madrid's 6-1 thumping of Galatasaray, Messi reminded everyone who is still the four-time reigning Ballon d'Or winner.
Despite boasting eight European Cup and Champions League crowns between them, Barcelona and Ajax had never met before their Group H encounter at the Nou Camp.
And typically it was a dazzling display from Messi that got the 2009 and 2011 winners off to the ideal start.
And the diminutive wizard dedicated the victory to Barca coach Gerard Martino, who will fly home to Argentina to attend his father's funeral.
"It was a special game. It is a shame what has happened and he is suffering, but we are all with him in this moment," he said.
Ajax are a far cry from the brilliant outfit that romped to their fourth title in 1995, just three years after Barca had broken their duck in the competition.
Messi's first had an air of inevitability about it as he was first felled on the edge of the area and then stepped up to curl home a sumptuous free-kick.
And his second came in another of Messi's classic moves as he took a pass from Sergio Busquets on the right before cutting inside onto his left foot to shoot home.
Centre-back Gerard Pique headed home a pinpoint Neymar cross from the left having stayed up for a corner.
But Messi didn't allow anyone else to hog the limelight for long as he fired home his third from Xavi's pass 15 minutes from time.
Things only got worse for Ajax as Kolbeinn Sigthorsson saw a penalty saved by Victor Valdes after Javier Mascherano had brought down Thurani Serero.
In the group's other game, AC Milan left it late before avoiding an embarrassing slip-up at the San Siro as Emilio Izaguirre's own goal broke Celtic's hearts, with Sulley Muntari adding a second to secure the Rossoneri a 2-0 success.
Jose Mourinho's Chelsea were stunned in the shock result of the night as FC Basel left Stamford Bridge with a 2-1 victory in Group E.
The hosts had seemed to be heading to a routine home victory when Brazilian Oscar put them ahead after quick, slick passes from David Luiz and Frank Lampard.
Oscar almost doubled the Londoners' advantage with a splendid second half strike that crashed back off the bar.
But then Mohamed Salah bent the ball around Ahsley Cole and inside the post on 71 minutes before Marco Streller headed home the unexpected winner from a corner.
Mourinho remained calm in adversity, saying: "I'm not in shock. The reality is that sometimes you don't win. I'm not happy of course. We have taken a step back in qualification but we have five games left to finish in the top two."
Schalke 04 took command of the group with three goals in the final quarter to beat Steaua Bucharest 3-0.
Japan's Atsuto Uchida, Ghana midfielder Kevin-Prince Boateng and German international Julien Draxler bagged the goals.
Last season's runners-up Borussia Dortmund had a disastrous start to their campaign as they went down 2-1 at Napoli in Group F.
It was a sorry night for the Germans, who thumped Hamburg 6-2 at the weekend, as coach Jurgen Klopp and goalkeeper Roman Weidenfeller were both given their marching orders after Gonzalo Higuain had given the Italians the lead.
Lorenzo Insigne doubled Napoli's advantage before an own goal from Camilo Zuniga late on gave Borussia scant consolation.
Arsenal joined Napoli at the top of the group with a 2-1 win over Marseille at the Stade Velodrome.
Manager Arsene Wenger said the first goal was crucial.
"I knew when it was still 0-0 after an hour that the team who scored first would win," he said.
Theo Walcott opened the scoring with a flashing volley before Aaron Ramsey continued his brilliant start to the season with his sixth goal of the current campaign, courtesy of a deflection.
Jordan Ayew scored a late penalty for the outplayed hosts after Ramsey spoilt his night by bringing down the Ghanaian's brother Andre Ayew.
Atletico Madrid made it a night to remember for the Spanish with a 3-1 win over visitors Zenit St Petersburg.
Miranda put them in front before powerful Brazil forward Hulk equalised. But goals from Arda Turan and Leo sent Atletico to the top of Group G, ahead of Porto, who won 1-0 at Austria Vienna thanks to Lucho Gonzalez's goal.
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