Palmer had almost identical left-footed goals from just inside the penalty area in the 22nd and 30th minutes, then sent a through pass that enabled João Pedro to chip goalkeeper Gianluigi Donnarumma in the 43d for his third goal in two starts with the Blues.
A 23-year-old who joined Chelsea from Manchester City two years ago, Palmer scored 18 goals this season.
PSG finished a man short after João Neves was given a red card in the 84th minute for pulling down Marc Cucurella by his hair. After a testy final few minutes, the teams needed to be separated as PSG coach Luis Enrique and Donnarumma pushed João Pedro near the center circle.
A heavy favorite who had outscored opponents 16-1, PSG had been looking to complete a quadruple after winning Ligue 1, the Coupe de France and its first Champions League title.
Before a tournament-high crowd of 81,188 at MetLife Stadium that included U.S. President Donald Trump, Chelsea showed the energy of a fourth day of rest after its semifinal, one more than PSG.
Chelsea had finished fourth in the Premier League and won the third-tier UEFA Conference League. The Blues took the world title for the second time after 2021, when it was an seven-team event. The Blues earned $128,435,000 to $153,815,000 in prize money, the amount depending on a participation fee FIFA has not disclosed.
PSG had not lost by three goals since a 4-1 Champions League defeat at Newcastle in October 2023.
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