Desai, who has just turned 35 and whose mother and fellow writer Anita was three times shortlisted for the Booker, won the literary award and its $93,000 cash prize for her novel "The Inheritance of Loss" on Tuesday.
The characters share an historical legacy and a common experience of inequality.
"Certain moves made long ago had produced all of them," Desai writes, referring to the economic and cultural power of the West.
Desai said after accepting her prize:"To my mother I owe a debt so profound. This book feels as much hers as as it does mine.
"It was written in her company and in her wisdom and kindness. I really owe her this book so enormously."
Desai, who was educated in India, England and the United States and took eight years to write the novel, divides her time between New York and New Delhi.
She said: "I have an Indian passport and given what the political climate has been in the United States, I feel more and more Indian."
Inheritance of Loss
The book, which is set in the mid-1980s, tells the story of a retired judge, his granddaughter, their cook and the cook's son, as a Nepalese insurgency erupts in their mountain town on the Indian side of the Himalayas.
The grandfather, a Cambridge-educated Anglophile, has his plans for a peaceful retirement at his crumbling house in the Himalayas shattered when his teenage granddaughter, an orphan called Sai, comes to live with him.
The grandfather is forced to confront his experience of racism as a student in England and his subsequent experience of returning to India and the young wife he abused.
"Certain moves made long ago had produced all of them"
Kiran Desai, "The Inheritance of Loss"
Sai is romantically involved with her maths tutor, Gyan, who rejects her privileged status and joins the Nepalese insurgents, while the cook pins all of his hopes on the son he sent to America.
The son, Biju, belongs to the "shadow class" of illegal immigrants in New York and moves from one poorly paid job to another, dodging the authorities.
Breadth and wisdom
Hermione Lee, the chairwoman of the judges, said: "It was a magnificent novel of humane breadth and wisdom, comic tenderness and powerful political acuteness."
Picking from a shortlist of relative unknowns after rejecting a string of literary heavyweights, Lee said: "The winner was chosen after a long, passionate and generous debate."
The award, which was founded in 1969, rewards the best book of the year by a writer from Britain, Ireland or a Commonwealth country.
The previous youngest woman to win the prize was Arundhati Roy, who won it in 1997 with her novel The God of Small Things when just a month short of her 36th birthday.
The youngest-ever winner was Ben Okri who won it in 1991 at the age of 32.