It was the former Borussia Dortmund forward's first goal for the Blues, but it wasn't long until he was celebrating a second before the break with a run and shot that deflected in off Ben Mee.
Pulisic then became the first American to snare an English top-flight treble since 2012 when he flicked home Mason Mount's cross.
By this point Chelsea were in cruise control and Willian added a fourth on 58 minutes to all-but seal the points.
Burnley had missed some gilt-edged chances through Ashley Barnes but finally got on the scoresheet with late strikes from Jay Rodriguez and Dwight McNeil.
The result means Frank Lampard's Chelsea have now won seven on the spin in all competitions and have bolstered their position in fourth, level on points with third-placed Leicester and five adrift of leaders Liverpool.
Next up, 11th-placed Burnley visit Sheffield United while Chelsea face a midweek League Cup clash with Manchester United before visiting Watford.
: Christian Pulisic of Chelsea celebrates with Willian of Chelsea after scoring his team's first goal during the Premier League match between Burnley FC and Chelsea FC at Turf Moor on October 26, 2019 in Burnley, United Kingdom.
Image credit: Getty Images
A big night for Pulisic. The 21-year-old has had a slow start to life at Chelsea and was even reportedly 'considering his future' due to his lack of action. However, Lampard has always insisted he had a big part to play going forward and his impact as a substitute in the midweek Champions League win at Ajax did not go unnoticed by the Blues boss. The American duly responded to his chance to impress here with his best showing in a Chelsea shirt so far. Pulisic was quite superb and capped his big evening with a perfect hat-trick that will have supporters licking their lips at the array of young talent Lampard appears to be getting the best out of.
MAN OF THE MATCH
Christian Pulisic (Chelsea). Followed up his lovely cameo and assist at Ajax in midweek with a match-winning performance in his 10th outing for the Blues. Direct with a real end product, he added an extra dimension to the visitors' attack that Burnley struggled to handle throughout.
21' - GOAL! Burnley 0-1 Chelsea. Pulisic pounces upon an error from Lowton and races towards the Burnley area. He takes on Tarkowski and drills a low shot into the far corner.
30' - BURNLEY CHANCE. Barnes somehow misses a sitter at the back post after Mee had headed a diagonal free kick into his path.
45' - GOAL! Burnley 0-2 Chelsea. The visitors win the ball high up the pitch once more. Pulisic drives at the heart of the Burnley defence and sees a low strike deflected into the net off Mee.
56' - GOAL! Burnley 0-3 Chelsea. Pulisic HAT-TRICK! The USA starlet is left free to flick a header into the far corner from Mount's pinpoint delivery.
58' - GOAL! Burnley 0-4 Chelsea. It's four! Willian jinks into the right side of the box and sizzles a low shot into the far corner.
77' - CHELSEA PENALTY AWARDDRAMA. The referee overturns his initial decision to give Chelsea a penalty following a VAR intervention. Tarkowski was adjudged to have tripped Hudson-Odoi, but replays showed minimal contact. Hudson-Odoi was then booked for simulation!
86' - GOAL! Burnley 1-4 Chelsea. Rodriguez thunders a dipping 35-yard strike beyond Kepa. It's a corker but only a consolation.
89' - GOAL! Burnley 2-4 Chelsea. McNeil pulls another one back for the hosts with a 20-yard drive that deflects off a defender on its ways into the net.
Pulisic is the first player from the USA to net for Chelsea in the PL. The Blues have now had players from 36 different nations score for them in the competition (excluding own goals).
Pulisic is the youngest player to score a Premier League hat-trick for Chelsea, breaking Tammy Abraham's record that stood for 42 days.
Burnley have only won one and lost 19 of their 26 Premier League meetings with established top-six sides.
Chelsea have scored two away Premier League hat-tricks in the same season for the first time since 1997-98 (Gianluca Vialli at Barnsley and Tore Andre Flo at Spurs).
Each of Chelsea's last 10 hat-tricks in all competitions have been scored by different players.
Pulisic is the first Chelsea player to score a 'perfect' Premier League hat-trick since Didier Drogba against Wigan in May 2010.