In a 1-2 finish for the Godolphin operation of Sheikh Mohammed bin Rashid al-Maktoum, Capponi (11-1) took second place three lengths behind under jockey Ahmed Ajtebi.
Planteur, a 14-1 shot ridden by Ryan Moore for Newmarket-based Marco Botti, finished third of the 13 runners.
Barzalona celebrated in the same flamboyant way he did after his success in last year's Epsom Derby on Pour Moi, standing up in his irons and raising his right arm high into the air as he crossed the winning line.
Monterosso was stepping up on his performance of 12 months ago when finishing third to Japanese winner Victoire Pisa.
The 11-8 favourite So You Think, trained by Aidan O'Brien in Ireland and ridden by his son Joseph, was in contention turning into the straight but was beaten into fourth, with German raider Zazou fifth.
The first two home were trained by Mahmoud al-Zarooni. It was a fifth success in the race for Godolphin since the event was inaugurated in 1996 but the first since 2006.
Sheikh Mohammed told reporters: "I am very happy that we won after so many years. Actually, even before the race I was a winner because we have here all these beautiful horses together and to race against them, that to me is a win.
"And look at these people, more than ever before. Dubai is full and Dubai is back."
Dubai, the Gulf Arab trade and business hub, has been recovering from its 2009-2010 debt crisis thanks to strong trade with Asia and inflows of tourists although bank lending remains slow and the property market weak.
Sheikh Mohammed, Dubai ruler and Prime Minister of the United Arab Emirates, said of his winner and runner-up: "When they came into the last corner and they were in front I was not sure that they would win.
"I thought somebody would come and catch them. When they crossed the line then I believed it."
Barzalona has now won the Epsom Derby and the world's most valuable race before the age of 21. He was signed by Godolphin earlier this month and is seen in the longer term as a likely successor to Frankie Dettori.
Dettori was beaten into seventh in Saturday's race on Prince Bishop but had two winners for Godolphin on the valuable support card.
The ebullient Barzalona told reporters: "I couldn't believe when no one was coming after me. This is a dream. I have no words to describe what I feel right now."
Asked about his extravagant celebration crossing the line he said: "I just had to. I had no choice."
O'Brien, 18, said of ex-Australian champion So You Think: "I had the ideal position behind the leader but he just didn't quicken on that surface. It was too dead for him."
There was disappointment for Chantal Sutherland, the first woman to ride in the race.
She partnered the well fancied Game On Dude for U.S. trainer Bob Baffert but could only finish 12th.
Sutherland, 36, told reporters: "He just got a little frazzled after not breaking so great."
1.African Story - F Dettori - S Bin Suroor - 5/6f
2.Viscount Nelson - K Shea - M De Kock - 12/1
3.Red Jazz - M Hills - C Hills - 10/1
1. Opinion Poll - F Dettori - M Al Zarooni - 10/11
2. Joshua Tree - J P Murtagh- M Botti - 16/1
3. Zanzamar- R Hills - M F De Kock - 18/1
4. Averroes - P Cosgrave - E Oertel - 50/1
1.Daddy Long Legs - C O'Donoghue - A P O'Brien - 7/1
2.Yang Tse Kiang - T Jarnet - R Chotard - 16/1
3.Wrote - R Moore - A P O'Brien - 11/4f
1.Ortensia - C williams - P Messara - 6/1
2.Sole Power - J Murtagh - E Lynam - 11/2f
3.Joy And Fun - B Doyle - D Cruz - 6/1
1.Krypton Factor - K Fallon - F Nass - 13/2
2.Rocket Man - F Coetzee - P Shaw - 3/1f
3.Lucky Nine - B Prebble - C Fownes - 13/2
1.Cityscape - J Doyle - R Charlton - 8/1
2.Mutahadee - C Soumillon - M De Kock - 9/2
3.City Style - M Barzalona - M Al Zarooni - 25/1
1.Cirrus Des Aigles - O Peslier - Mme C Barande-Barbe - 11/4
2.St Nicholas Abbey - J O'Brien - A P O'Brien - 9/4f
3.Jakkalberry - R Moore - M Botti - 33/1
1.Monterosso - M Barzalona - M Al Zarooni - 20/1
2.Capponi - A Ajtebi - M Al Zarooni - 11/1
3.Planteur - R Moore - M Botti - 14/1