Ten-year-old Rhea has been named Child Genius 2016 in a nail-biting final that host Richard Osman hailed the "greatest in the history of the show".
The west London schoolgirl, whose surname has not been revealed, shot ahead at the beginning of the round with six correct answers to her opponent Saffy's two, but the girls drew equal on nine points as they entered the final head-to-head question.
Rhea, who moved with her family from the US six years ago, correctly spelled the word "eleemosynary", meaning relating to charity, to claim the Child Genius title at the end of four weeks of competition on the Channel 4 show.
Osman told her the audience were "gasping" as the pair quickly calculated sums including "14 times 3, minus 16, times 3, divided by 2, plus 44", and answered questions on everything from the nationality of composer Gustav Holst to the year the American Constitution was approved by Congress.
He said: "I'm going to go on record and say that was the greatest final in the history of Child Genius."
Speaking of her win, Rhea said: "It's meant getting up early, going to sleep late, studying. It just feels really, really great."
Her place in the final was secured by her mother Sonal - who gave up her job as an obstetrician to train Rhea - who queried an incorrect answer that she had given during her specialist subject round on Florence Nightingale's influence on military and healthcare reform.
Independent adjudicator Olivia van der Werff agreed the question had been too general and accepted Rhea's answer of Dr Duncan Menzies to the question, "To which medical officer did Florence Nightingale report to in the Crimea?" which brought her equal to Saffy on 16 points, whose specialist subject was Margaret Thatcher's premiership and tax policy.
It meant Birmingham-born Stephen came third with 15 points on degree-level questions on spiders that mimic insects while his sister Georgia, 10, came fifth in the competition after answering 11 correct questions on Russian ballet and the career of Rudolf Nureyev.
Twelve-year-old Jonathan, from Gloucester, came fourth with questions on public health and sanitation in the Victorian era.