Alamshar, who was third in the Epsom Derby, and Dalakhani, unbeaten in six outings before Sunday's race, were left to battle it out as the furious pace left the field trailing with the two horses running neck-and-neck two furlongs from home.
But Murtagh, wearing the green and red silks of the Aga Khan, rode an almost perfect race as Alamshar, the 4-1 second favorite, proved the stronger. Dalakhani, 7-4 odds-on favorite finished second with Roosevelt, a 150-1 outsider, third.
"It was just pure magic," said Murtagh, who raised his arms in triumph in front of the grandstand. "There was only going to be one winner. He (Dalakhani) might be king of France but he's on our turf now," he told the BBC.
Alamshar's victory, achieved by the same Oxx-Murtagh combination that won the race with Sinndar in 2000, gave the Aga Khan his fifth Irish Derby triumph and brought him level with the number of successes enjoyed by his grandfather.
Dalakhani, the Daarshan colt trained in France by Alain de Royer-Dupre also for the Aga Khan, failed to live up to his billing as he faltered under the blistering pace.
The favorite, ridden by 23-yar-old Belgian-born Christophe Soumillon, had seemed perfectly placed to notch up a seventh straight win as he sat comfortably behind Handel and High Country, two of Irish trainer Aidan O'Brien's six-strong team.
But he was found out in the home stretch as Murtagh, who had to shake off a back problem before the race, used his experience to guide Alamshar first past the post and dash Dalakhani's claims to be Europe's leading three-year-old.
"You see the way he (Alamshar) gets his head down and gallops," said Murtagh. "For a small horse he's all heart. John Oxx has done a great job. It was just magic."
Alamshar's win also ended O'Brien's bid to become the first trainer to win the race three years in a row, following High Chaparral's success last year and Galileo's in 2001. O'Brien had to be content Colm O'Donoghue's third place on Roosevelt.
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