As the pack entered the final straight it was a clear fight between the Henry Cecil trained Beat Hollow and Sakhee.
The final furlong saw a neck-and-neck contest between the much fancied Sakhee and the Jon Oxx trained colt.
It was Ireland's first win in 16 years and for much of the race it looked as if Sinndar would be outrun by Sakhee and pre-race favourite Beat Hollow, who eventually finished third.
The race started in frantic fashion with Kingsclere straying wide and acting as a pacemaker, as the colts sped to a tremendously quick time over the first furlong.
Clear fight
But slowly the Hamdan Al Maktoum horse contested for the lead alongside Best of the Bests, which was ridden by Amercian Chris McCarron.
As the pack entered the final straight it was a clear fight between the Henry Cecil trained Beat Hollow and Sakhee.
But a late burst on the outside by the Irish horse ended both the American jockey's dreams and also Cecil's ambition of winning a second successive Oaks/Derby double.
Sinndar's trainer John Oxx was delighted with the victory.
"He is a horse that I have always liked," said Oxx.
"It's typical the way he won because he never wins by much but he's very hardworking.
Ecstatic
"We were hopeful he would run well but you never can tell until the race itself."
Jockey Murtagh was ecstatic, having won his first Derby in four attempts.
"It's a real privilege to win this as John Oxx and the Aga Khan have been very supportive in my career," said Murtagh.
"Great Irish jockeys have won this race and I feel so lucky to be part of their club."
Winning owner The Aga Khan, who has recently ended his boycott of English racing, was also in jubilant mood.
"It's a great race to win it's the classic of three-year-old European racing," he said.
"He's always been a horse that John Oxx liked."
Finishing order
1st Sinndar (J P Murtagh)
2nd Sakhee (R Hills)
3rd Beat Hollow (T Quinn)
4th Best Of The Bests
5th Wellbeing
6th Hatha Anna
7th St Expedit
8th Barathea Guest
9th Zyz
10th Aristotle
11th Inchlonaig
12th Broche
13th Going Global
14th Cracow
15th Kingsclere
Winning trainer: John M Oxx (Ireland)