The United States international grabbed his first goals in Chelsea colours since completing a £58 million ($75m) move from Borussia Dortmund earlier this year, on his first start since August.
The 21-year-old opened the scoring with a brilliant individual effort just after the 20-minute mark, before repeating the trick just before the half-time whistle.
Pulisic added a third early in the second period, improvising with his back to goal to head a pinpoint Mason Mount cross past Nick Pope and into the net.
Willian added a fourth for Chelsea before Burnley hit two late consolation goals through Jay Rodriguez and Dwight McNeil, with Frank Lampard's men moving back into the top four after a fourth straight Premier League victory.
The Blues boss has only used Pulisic sparingly since the start of the season, but Tomori was delighted to see the midfielder build on a superb cameo during a 1-0 Champions League win at Ajax last week with a hat-trick against the Clarets.
“Everyone is disappointed when they don’t play," Tomori told the Evening Standard. "We have got a lot of talented players, so you just have to be patient and when you get your chance you have just got to take it like he did on Saturday.
“I am really happy for him — that patience and hard work he showed in training has paid off. You have got to be on top of your game, not only in the games but in training as well.
“It is good Christian has come in because everyone has to be on their toes. No one knows their position is safe and that drives the team on and brings the best out of each individual.”
Chelsea have emerged as a major force once again after recording seven wins in their last seven matches across all competitions, with Lampard boasting a squad full of promising young talent.
Callum Hudson-Odoi has been among those to make a significant contribution since his return from injury, but the England international had to make do with a substitute appearance at Turf Moor.
Tomori thinks strong competition for places at Chelsea will help raise the overall level of the team, as he added: "Callum was rested on Saturday and Christian comes in and scores a hat-trick.
“That is going to raise Callum’s game and then Christian is going to want to keep raising his game to stay in the team.
“We have a young team, an exciting team, and we all try to help each other out as the games go on and in training. We don’t feel like we are young players, we are just trying to improve ourselves and to keep our places in the team.”