Robert, who had led throughout the four-day competition, knocked down the final fence of an eight horse jump-off on USA Today.
It left him tied with Ellen on overall points, but her time of 48.10sec aboard Equimax Ocolado was more than three seconds clear of the field.
"Equimax Ocolado jumped out of his skin and was so careful every step of the way," said Ellen, who collected £25,000.
She had also collected top honours at the Horse of the Year Show on the same horse six months ago.
"This is one title I have been chasing for a while," Ellen said.
"It is one I really wanted to win, so I am ecstatic with the result."
She became the first female Open champion since Ireland's Jessica Kuerten in 2007, and it has set her up for potential further successes this year as the build-up begins gathering momentum towards London 2012.
Her previous best Open performance had been sixth last year.
For Robert though, there was only agony after seeing his hopes of the top prize slip away during a nerve-shredding conclusion.
"I am disappointed, but it is just how showjumping goes," he said.
"One pole down can make all the difference.
"My game-plan was to go clear, but looking back, with a jump in hand, maybe I should have gone faster.
"I decided to ride USA Today in the final rather than Casino because he had been jumping so well all week and I know he has the ability to beat any horse in the Championship.
"He was really unlucky to have the last pole down."
Robert had to be content with a runners-up prize of just under £10,000, while third place went to Holland's Eric van der Vleuten with Utascha SFN, who won the Rolex World Cup qualifier at Olympia almost four months ago.
Ellen Whitaker had earlier claimed an emphatic victory in the show's penultimate international class.
She guided Kanselier home in the Zinc Event Management British Speed Stakes, collecting a £6,000 first prize.
The in-form combination never came under serious threat, with second-placed Tina Fletcher and Promised Land almost three seconds behind.
Laura Renwick, last year's speed stakes winner, took third aboard Vernon G, clocking 53.39, while Gulliksen on Storm was fourth.
Showjumping attention now switches to the World Cup final in Geneva, which starts on Wednesday.
Michael Whitaker - Ellen and Robert's uncle - is the solitary British qualifier among a 43-strong field from 19 countries, including the likes of Brazilian star Rodrigo Pessoa, reigning European champion Kevin Staut and German aces Ludger Beerbaum and Marcus Ehning.
Story provided by www.insidethegames.biz
– Pauline Courtois leads after first day
World Weightlifting Championships