After a goalless opening half, the Blues killed off their opponents with a devastating three goals in eight minutes, courtesy of that Havertz double and an opener from Reece James.
While Burnley's survival will not be decided against top-level opponents like Chelsea, the manner of the second-half collapse will have irked manager Sean Dyche.
Story of the match
Dyche made two changes from the defeat against Leicester City in midweek. In came Jay Rodriguez and Nathan Collins for Maxwel Cornet and Ben Mee – who had hobbled off on Wednesday night – but the Clarets' skipper was fit enough to make the bench.
This was the first league match for Chelsea following chairman Roman Abramovich’s decision to sell the club.
You have to feel for Tuchel, leaving the melodrama of Paris Saint Germain in the hope of a purer level of coaching, but he has since had to deal with the fallout over the European Super League, a petulant Romelu Lukaku, and now the departure of Chelsea’s long-serving owner.
As Turf Moor stood to applaud in solidarity with Ukraine before kick-off, a large number of visiting supporters bizarrely chose to chant Abramovich's name. It's a strange time for fans of the Blues at the moment but history won't look back on that moment with fondness.
The Londoners made quite a tepid start to the match in East Lancashire. However, they did nearly take the lead on 15 minutes when James fizzed Saul's cross towards the far corner. Nick Pope was beaten but Charlie Taylor did well to make a sliding block on the line.
Moments later, Aaron Lennon burst in behind Saul and Antonio Rudiger before finding Wout Weghorst with a low drilled cross. The big-man made a good first-time connection but Thiago Silva was on-hand to make another goal-line clearance.
As ever, the Chelsea system allows wide centre-backs like Rudiger to play a part in the attack. And the charismatic defender had two efforts on goal: the first requiring an easy save from Pope and the second engineering a brave block from Collins.
The best chance of the opening half-hour fell to Burnley, though, and Dwight McNeil really ought to have done better with it. Edouard Mendy flapped at Ashley Westwood's looping cross but the 22-year-old spooned the loose ball over from point-blank range.
Chelsea had received almost 80% of the first-half possession, though their struggles to break down an organised Burnley block were clear to see.
Jorginho did nearly provide that penetration but his fierce effort from 20-yards was headed away by Collins.
Tuchel would have asked for more decisiveness, during the interval, but even the German couldn't have asked for a better response – taking the lead inside two minutes of the restart.
James found himself advanced in the Burnley box with a plethora of bodies in front of him. He stood-up McNeil, turned him inside and out, before squeezing a shot through a rack of bodies and into the far corner. It was a superb bit of play from the wing-back.
On 53 minutes, the Blues doubled down on that advantage.
Pulisic fired a swerving, dipping ball to the back-post and an unmarked Havertz simply nodded the ball in from six-yards. The former Bayer Leverkusen man netted when these teams met at Stamford Bridge in November and he wasn't done yet.
Just a couple of minutes after his first, the attacker bundled James' cut-back over the line to put Chelsea three ahead. The Burnley defence was all at sea once again as the European Champions demonstrated their true power.
Burnley responded just after the hour mark by bringing Cornet on for Rodriguez but the match had already gone.
However, on 69 minutes, there was time for one more blow against the battered and bruised Burnley jaw.
Saul found space to deliver a low cross and Tarkowski inadvertently prodded the ball forward for Pulisic. The American couldn't believe his luck as he slammed the ball into the back of the net.
In the other camp, Dyche's decision to bring Ashley Barnes on for Weghorst in the 78th minute seemed to be a case of saving a key player for another day.
The result sees Chelsea push further away from the teams battling for fourth; they are now six points ahead of Manchester United with a game in hand.