The 4-6 favourite, ridden by Pat Smullen for trainer Dermot Weld, held off the challenge of Idaho, with outsider Stellar Mass third.
Harzand, owned by the Aga Khan, is the 18th horse to complete the Epsom-Curragh double.
A son of 2009 Epsom champion Sea The Stars, Harzand won by half a length from the Aidan O'Brien-trained Idaho.
The winner is now likely to be aimed at the Prix de l'Arc de Triomphe, a race won by his father, in October.
Stablemate Ebediyin set the pace before Smullen guided his mount to the front.
Idaho, under Ryan Moore, laid down a stern challenge at about two furlongs out but Harzand battled to victory after a stirring duel.
Smullen said: "He's such a great horse, he's got such courage and determination.
"Ryan (came with one good determined run, I needed this horse to dig deep for me and he did - how good is he?
"This matches Epsom, in front of our home crowd. The pressure was on and we pulled it off."
Analysis - Correspondent Cornelius Lysaght
"Another outstanding performance from Harzand to do the Derby double.
"As at Epsom, another runner put it up to the son of champion racehorse-turned top stallion Sea The Stars, but, also like June 4, this colt was having none of it, demonstrating he was truly a chip off the old block.
"And though the winning margin of Harzand over Idaho - who got level - was a half-length, it was a little more comfortable than the bare facts suggest. He goes to the 'Arc' in October, which his Dad won in 2009, with a definite chance."
Harzand won the Irish Derby at the Curragh to seal a Derby double after his triumph at Epsom earlier in June.