The U.S. international was named in the starting XI after his impactful role off the substitutes' bench in Chelsea's 1-0 win over Ajax in the Champions League on Wednesday.
Pulisic had struggled to get minutes since arriving at Stamford Bridge in the summer following his €64 million transfer from Bundesliga side Borussia Dortmund, but he made his mark in the first half against Burnley.
Both of the 21-year-old's first-half goals came off stellar individual efforts after hard-charging runs from the midfield. The first was a left-footed shot after Pulisic beat his defender in the penalty area. The second was an equally impressive finish, this time with his right foot and with the help of a deflection off Burnley defender Ben Mee.
The pair of goals staked Chelsea to a 2-0 lead at half-time. Pulisic added his third early in the second half and Willain added another to give Chelsea a comfortable lead at Turf Moor.
The American becomes just the second player from the U.S. to score a hat trick in the Premier League, joining Clint Dempsey, who did it in 2012 for Fulham in a match against Newcastle.
As an added bonus, Pulisic scored a goal with his right foot, his left foot and from a header, making it a perfect hat trick to become the first Chelsea player to complete the feat since Didier Drogba against Wigan in May 2010.
Burnley added two late goals, but the damage had been done by Pulisic and Chelsea, who took all three points and maintained their spot in the top four of the Premier League table.
Chelsea manager Frank Lampard addressed Pulisic's lack of playing time earlier in October, saying he had to make "harsh" decisions in his lineup sometimes, but added Pulisic's time would come.
Lampard said: "Sometimes I have to make harsh decisions and say something that I see can help their game but might not sound that nice because I want them to be the best, all of them. That's what I want them to be. That's part of the process.
"Christian Pulisic has a price tag. Ross Barkley is an international player. Mason Mount is an international player, Callum Hudson-Odoi just signed a new contract, Bayern Munich wanted to buy him last summer. He's an international player."