Preti Taneja's We That Are Young, which has moved the action to India, was described as "awe-inspiring".
Sarah Perry, chair of judges, said Taneja's ambition was "breath-taking".
The prize recognises debut novelists, with the runners-up being Gail Honeyman, for Eleanor Oliphant is Completely Fine, and Paula Cocozza, for How to Be Human.
'What will come next?'
Perry and her fellow judges, broadcaster Samira Ahmed and Waterstones' head of fiction Chris White, said the three shortlisted works were "bravely and urgently about the way we live now".
She added of Taneja: "I loved the sheer ambition of the book - the idea that for her first book, she said: 'I'm going to rewrite King Lear as a multi-voice novel, set in contemporary India'.
"It's awe-inspiring, and she totally managed to carry it off. It's just incredible. The fact it had such huge ambition is breath-taking."
Perry said it was a "richly compelling and vividly peopled novel", that was full of "tasty detail" and texture.
She added that the judges found themselves shaking their heads, asking: "If this is her first novel, what extraordinary work will come next?"
Taneja, a human rights activist and academic, wins a £10,000 prize, which is to go towards work on the author's second novel.
Her debut is set against the backdrop of the 2011 anti-corruption riots in India. It tells the story of what happens when an ageing patriarch, Devraj, leaves his company to his daughters Gargi, Radha and Sita.
The prize was set up in memory of publisher and literary agent Desmond Elliott, who died in 2003.
Previous recipients include Eimear McBride, Francis Spufford, Ali Shaw and Claire Fuller.
We That Are Young and McBride's A Girl is a Half-formed Thing were both published by Galley Beggar Press, an independent publisher run by a husband-and-wife team.