The west London schoolgirl beat nine-year-old Saffy by spelling the word "eleemosynary", meaning charitable.
Rhea got through to the head-to-head after her mother contested an incorrect answer during her earlier specialist round about Florence Nightingale.
Independent adjudicator Olivia van der Werff later ruled it was acceptable.
The dispute centred on the question: "To which medical officer did Florence Nightingale report in the Crimea?"
Rhea's answer Duncan Menzies was initially deemed incorrect. But her mother Sonal, who gave up her job as an obstetrician to help educate Rhea, successfully argued that Nightingale effectively reported to every medical officer.
The programme was watched on Channel 4 on Tuesday by an average of 1.3 million viewers, not including +1, according to overnight ratings.
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Ten-year-old Rhea has been named Child Genius 2016 after her mother intervened to dispute one of the answers in the Channel 4 show's final.