The Germany international had struggled to impress in his opening matches in a Chelsea shirt after a £72.7million move to Stamford Bridge.
His manager Frank Lampard had suggested it would take time for Havertz to adapt to his new surroundings in the buildup to the clash with Barnsley but he was on fire against the Championship side.
It was Tammy Abraham – who was also in fine form – who opened the scoring. The England striker pinched the ball off a defender and slotted home.
Abraham was involved again as Havertz doubled the lead. A smart dummy allowed the ball to roll through to the German who slotted his first Chelsea goal home.
Ross Barkley put the tie to bed early in the second half with a cool slotted finish before Havertz added his second and Chelsea’s fourth in the 55th minute to put the contest further beyond Barnsley’s reach.
Havertz scored his third of the night – and the first hat-trick of his professional career – as he beat Barnsley keeper Bradley Collins in a foot race and then passed the ball into the empty net.
It proved to be his last involvement of the night as Lampard hooked him off for fellow Chelsea new boy Ben Chilwell and he was embraced warmly by his manager as he went for a well deserved rest.
Speaking about Havertz’s performance after the match, Lampard said:’I was delighted with Kai and everything of the night that I wanted from him.
He added: ‘It was a great exericse for him, another game to see how we want to work off the ball, but also have freedom on the ball and combinations with Tammy [Abraham]. It’s the first of many great nights for him.’
Olivier Giroud scored a sixth late on, guiding it home after a smart ball in from debutant Chilwell.
Chilwell was delighted to make his debut for the Blues and he also gave a special shoutout for Havertz after his heroics.
‘Debut and assist,’ Chilwell posted on Twitter.
‘Great team performance, well done lads!
‘Shoutout Kai Havertz on the hat-trick.’