The Americans’ total of 172.33 was almost six full marks ahead of Russia in second, with Italy beating China to a surprise bronze in Stuttgart.
Great Britain finished sixth in Germany, with Olympic qualification for Tokyo 2020 already confirmed.
Biles finished with a personal total of 59.733 in winning her 15th world title.
The 22-year-old was the outstanding performer in a team that included Jade Carey, 19, and 16-year-olds Sunisa Lee, Kara Eaker and Grace McCallum.
“I never think of records – I just go out there and do what I came to do,” said Biles.
“Every year it feels better and better, just because we’re adding to the legacy.”
Victory sees her overtake Russia’s Svetlana Khorkina as the most decorated woman in the competition’s history.
Biles has three silvers and three bronzes in addition to her 15 golds while Khorkina managed nine golds, eight silvers and three bronzes.
Biles is again competing in all six finals, having become the first women since 1987 to win a medal in all six events at the last year’s Worlds in Doha.
The Texan now has the chance to become the gymnast with the most medals overall in World Championships history.
She needs three more this week to overtake Vitaly Scherbo’s tally of 23, which he won for the Soviet Union, the Commonwealth of Independent States and Belarus in the 1990s.
The British women’s round was mixed, although they still improved on their qualifying position in the final.
Becky Downie was the star turn with a superb 14.9 score on uneven bars.
“That’s a really good result for us – we came into it with nothing to lose,” she told BBC Sport.
“We didn’t make the team final last year so just to be in this was a huge step forward for us.”
Downie, younger sister Ellie (vault) and Alice Kinsella (all around) will appear in finals again over the coming week.