Saeed bin Suroor's colt took a big leap forward from winning a Doncaster maiden (where he beat the promising Turgenev) to taste Group One success as he burst clear of the Freddy Head-trained Anodor.
Murphy, who has had an outstanding season, settled his mount in second behind Aidan O'Brien's Broome, who set a brisk pace up front.
Murphy sent the son of Raven's Pass into the lead a furlong out and kept up the gallop to score by a neck from Broome, with Anodor only third having had every chance.
Bin Suroor said: "The two-year-olds this year have done really well and Royal Marine has been good since he won at Doncaster last time.
"I talked to Sheikh Mohammed and he made the decision to run him in this race. Now I have to go back to him again to ask about his future.
"We'll get him back to Dubai. What I like about him is he stays well, but he also has plenty of speed.
"I thought Oisin Murphy gave him a very good ride as the horse took a strong hold."
He added: "He's a big, strong horse and in the future he could be anything.
"He's still a baby and he will be better in the future. We'll talk to Sheikh Mohammed and make a decision about what we are going to do.
"Sheikh Mohammed sent me nice horses this year. I'm very positive for the future."
O'Brien said of Broome: "He's finished for the year, but he's a horse that I'm really looking forward to.
"I don't think he was finished - he was coming back at them a bit at the end."