The 16-1 shot, trained by Charlie Appleby and ridden by William Buick, dominated the 239th running of the race to scoop the 920,000-pound first prize ahead of second-placed Dee Ex Bee (20-1) and Roaring Lion (6-1) in third.
Hot favourite Saxon Warrior could finish only fourth in the 12-horse field.
"It is not easy to win the Derby but we did it," said Sheikh Mohammed.
The win represented sweet revenge for Masar, who had been beaten into third in the 2000 Guineas by Saxon Warrior last month.
Aidan O'Brien's horse had been hoping to complete the second leg of racing's Triple Crown at Epsom, ahead of an attempt to win the St Leger in September.
But the three-year-old, one of five runners trained by the Irishman, was hampered by an inside draw and never recovered from being boxed in at the start.
Masar, with Buick in Godolphin's royal blue colours, forced his way to the front mid-race and never looked like being caught.
"It's not sunk in yet," Appleby said after training his first Derby winner.
"I'm delighted for His Highness Sheikh Mohammed. Firstly for giving me the position to be here. I’ve always said when I started this job I wanted to be the first person to have a Derby winner in Godolphin blue."
It proved a one-two for the Dubai royal family, with second-placed Dee Ex Bee owned by Sheikh Mohammed's son, Sheikh Hamdan.
(Reporting by Neil Robinson; Editing by Christian Radnedge and Clare Fallon)
Share
