Dermot Weld's three-year-old, who overcame a late injury scare, was a 13-2 shot for the world's most famous flat race and was ridden by Pat Smullen.
The son of 2009 Derby winner Sea The Stars hit the front with more than a furlong to run, with US Army Ranger and Idaho pushing hard.
But Harzand beat the favourite by a length and a half with Idaho in third.
"I spotted the white face of US Army Ranger, but this horse responded to me," Smullen, 39, said.
Harzand, winner of the Ballysax Stakes at Leopardstown in April, had been a doubtful runner on Saturday morning after spreading a plate - when the horseshoe becomes detached from the hoof.
"The trouble we had with him this morning, I didn't know if he would get here, but it's a great team effort. I'm delighted for them." Smullen added.
Winning owner-breeder Aga Khan, had previously tasted Derby glory with horses including the legendary Shergar and most recently Sinndar in 2000.
It was also a first derby triumph for two-time Melbourne Cup winning trainer Weld.
"I won my first Classic here with Blue Wind many moons ago, when I probably didn't have horses like this to win this great race," Weld said.
"It's wonderful to do it. We had a huge worry this morning as he spread a plate travelling over and he was a very doubtful runner right up to about an hour ago.
"But with the tremendous help of all my colleagues and my team, we made it."
Cornelius Lysaght, BBC Sports racing correspondent
"Tremendous stuff from Harzand as he swept aside concerns following a late foot scare and dug deep to see off the fast-finishing favourite, so recording a fifth Derby success in the Aga Khan silks, once ubiquitous in Britain but rarely seen these days.
"The owner prefers to concentrate on racing in France and Ireland where Dermot Weld has his base a stone's throw from the Curragh training grounds.
"From there, he's planned major-race raids around the world, and though there's no indication the 68-year-old's anywhere near slowing down, Pat Smullen expressed the view it would be 'a travesty' if he had retired without an Epsom Derby win."
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Harzand held off the challenge of favourite US Army Ranger and Idaho to win the Derby at Epsom.