Biles had to settle for a disappointing silver, while her American teammate Jordan Chiles claimed bronze.
Biles was heavily favoured coming into the final given the difficulty of her high-flying routine but landed with two feet out of bounds on two of her four tumbling passes.
She paid a heavy price for those mistakes as the deductions she incurred denied her what would have been her fourth gold medal of these Games.
Andrade claimed the top prize for producing a near flawless, albeit less difficult, routine which was rewarded with a 14.166 from the judges.
Biles' routine got off to a promising start when she nailed her triple-twisting double back but the power she generated during the tumbling sequences left her completely stepping out of bounds on her next attempt.
She again found herself out of the marked area on her final pass, with the errors automatically incurring her a deduction of six tenths of a point.
It left her anxiously looking up at the scoreboard and when her mark of 14.133 flashed up, she found her name below Andrade's on the standings. She lost the gold medal by just 0.033 of a point.
The final day of the artistic gymnastics programme did not end the way Biles would have wanted as she also suffered disappointment in the balance beam final, finishing fifth after slipping off that apparatus.
Despite the less than ideal finale, the Paris Games still marks a triumphant comeback for the 27-year-old Biles, who led the U.S. to the team title and won the all-around and vault gold medals.
She withdrew from the Tokyo Games three years ago suffering with a mental block known as the "twisties" - a temporary loss of spatial awareness experienced by some gymnasts when completing high-difficulty elements.
Her withdrawal caused concern among her vast fan base about whether she would ever set foot on the Olympic stage again as Biles took a two-year break from the sport.
She returned healthy, happy and as dominant as ever as she qualified for her third Games and has not ruled out competing at the Los Angeles Games in 2028.
