Seamus Heffernan also won the race on Soldier of Fortune last year
Aidan O'Brien became the first trainer to win the Irish Derby three years in a row after Frozen Fire claimed a surprise win at The Curragh on Sunday.
Jockey Seamus Heffernan timed his run to perfection as the 16-1 chance came through the field with a furlong to go.
After a stewards' inquiry, favourite Tartan Bearer was promoted to third place with Casual Conquest in second.
O'Brien's victory was his sixth in the race, bringing him level with legendary namesake Vincent O'Brien.
"It's unbelievable," said Aiden O'Brien, who won the race with Dylan Thomas in 2006 and Soldier Of Fortune last year.
"We always thought this horse had a lot of class and Seamus gave him a very good ride.
"This is down to a lot of people - it's been a privilege to have been involved in it.
"Seamus has worked very hard and is a great judge of a horse. Nobody deserves it more than Seamus and I couldn't be happier for him.
"This is marvellous. The race was a full, solid mile-and-a-half and there are no excuses.
"All of ours have run great races, but I think Alessandro Volta got stage-fright when he turned into the straight - he wouldn't have seen a crowd like that in front of him before.
"The Curragh is probably the greatest racecourse in the world as it is a very fair track and really tests a horse."
Hindu Kush made most of the early running as the genuine contenders bided their time, and Johnny Murtagh's Alessandro Volta took over at the head of the pack as the race began to enter the final stages.
It looked to be a straight foot race between even-money favourite Tartan Bearer, Alessandro Volta and Curtain Call, but Murtagh's mount suddenly veered left.
Curtain Call seemed to be the worst affected and Frozen Fire was in the right place at the right time to seize control of the race and surge to a two-length victory.
"Aiden always trains them for the big day and this is a big day," said Heffernan.
"I was riding him to try to get placed and he is a bit weak but I was happy to get a lead and follow some of the fancied ones.
"It's unbelievable to win this two years in a row - it's a dream."
The stewards demoted Alessandro Volta from third place after the race.
Ante-post favourite New Approach was withdrawn on the morning of the race with a bruised foot, denying Jim-Bolger's horse the chance to become the first to complete the English-Irish Derby double since 2002.
Irish Derby result:
1. Frozen Fire (J A Heffernan) 16-12. Casual Conquest 4-13. Tartan Bearer Evens fav4. Curtain Call 8-1
11 ran

Mr Alner trained the 1998 Gold Cup winner, Cool Dawn
A trust fund in aid of a Dorset trainer who broke a bone in his neck in a car crash has been launched.
Robert Alner suffered life-threatening injuries after his car collided with a telegraph pole in Dorset last November.
Many of the biggest names in jump racing were at the fund's launch and the trainer's wife Sally said the family were "deeply touched".
"Both of us are overwhelmed by all the support Robert has received since his accident," she said.
"People have been amazing and the Injured Jockeys Fund has been there for Robert from day one.
"We can't thank everyone enough for all their efforts and are deeply touched that a fund has been set up for him."
Alner's long-time stable jockey Andrew Thornton is one of the trustees.
He said: "There are lots of practical things we can do to make Robert's life a little easier when he resumes back at the yard.
"Unfortunately most of them cost money. That's why we are launching a fund to help him."
Alner, 64, suffered serious neck injuries in the accident and is continuing to make steady progress at Odstock Hospital, near Salisbury.
The Robert Alner Fund has already been boosted by contributions from a dinner dance at Cheltenham racecourse in January.
Lambourn trainer Charlie Mann is organising a golf day on 30 June while champion trainer Paul Nicholls handed over his winning percentage from his hunter chase victories this season.
A special ball at Wincanton racecourse on 11 October is also planned

The outbreak will cost the industry millions of dollarsEight Australian racehorses have tested positive for equine influenza, forcing the suspension of Sydney's spring carnival racing.
The horses are based at Randwick racecourse in Sydney, the headquarters of racing in New South Wales.
The racecourse will be quarantined for 30 days to try to contain the outbreak.
The flu was first detected in recreational horses in Sydney last week, forcing a ban on horse movements and the cancellation of race meetings.
The primary industries minister for New South Wales, Ian Macdonald, said the flu could spread quickly through the Randwick stables, where some 700 thoroughbreds are based.
Some of Australia's finest thoroughbreds are stabled at Randwick and it is also home to some of the country's leading trainers.
The flu was found in eight of 10 horses from the stable of Randwick trainer Anthony Cummings.
'Grim day'
The outbreak is devastating blow to the racing industry, reports the BBC's Nick Bryant in Sydney.
The suspension of racing will cost millions of dollars, not just to the horse industry but to the bookmakers. There are fears of major job losses.

Jobs at the Randwick racecourse are threatened"It is more than a disaster, it is a grim, black day," Racing New South Wales Chief Executive Peter V'Landys told reporters.
He said the cancellation of Sydney races would have a significant impact on the Melbourne spring carnival, including the Melbourne Cup, Australia's most prestigious horse race which takes place in November.
"The cream of the horses are based at Randwick and Warwick Farm (in Sydney). You have leading trainers at Randwick. None of those horses now will be able to compete in Melbourne," he said.
Meanwhile, about 100 people, 30 of them children, remained quarantined following an outbreak in Warwick, Queensland state. Equine flu does not affect humans, but can be carried on clothing or footwear.

Sakhee's Secret has now won four races in a rowSakhee's Secret won his fourth race in a row by taking victory in the Group One July Cup at Newmarket on Friday.
Steve Drowne's 9-2 mount beat Dutch Art by half a length, with 16-1 shot Red Clubs one and a quarter lengths back in third place in the six furlong race.
"He's a youngster and is as good as I've ridden," said Drowne afterwards.
Bentley Biscuit had another poor day, coming home 10th out of 18 runners, and Soldier's Tale was withdrawn before the race because of the going.
July Cup result:1 Sakhee's Secret (S Drowne) 9-22 Dutch Art (J Fortune) 5-13 Red Clubs (M Hills) 16-118 ran