The Brazilian hit his three goals in the space of 13 minutes in the 6-1 win over Celtic to open his account for the Catalan club in European competition
With Lionel Messi still sidelined through injury and Cesc Fabregas suspended, Neymar started in a central role for the Blaugrana and was a constant threat for the Spanish champions.
The Brazilian, who had failed to net in his previous five Champions League appearances, set up Pedro for the second goal before hitting a 13-minute hat-trick either side of the interval as the Catalans ran out 6-1 winners at Camp Nou.
"I'm very happy with my first three goals in the Champions League," Neymar told Canal Plus straight after the game. "I didn't feel pressure, but wherever I play, I prefer to play with independence."
That independence came about partly because of the Brazilian's move to the middle of Barca's attack, but also due to some dreadful defending by the visitors.
The 21-year-old was left all alone to tap home his first following a wonderful team move, waltzed through the Scots' back line for his superb second and nutmegged Efe Ambrose before slotting in his third
The treble was the fourth-fastest Champions League hat-trick - some five minutes slower than Lyon's Batefimbi Gomis against Dinamo Zagreb in December, 2011.
Barca's comfortable win sees them top Group H ahead of Monday's last-16 draw.