Godolphin's Alexandros emerged as the winner's main challenger in the final strides but it was Virtual who passed the post narrowly in front.
A delighted Fortune admitted: "I thought he'd got me - I felt sick going across the line.
"But this lad stuck his neck out, and must have just got him on the line. He needed the race the last day, and everything was in his favour today."
Gosden said: "It was a stunning finish, because from my angle it looked like we had been beaten a short head. Going past the line he was a full head in front but on the line Jimmy thought he had been done.
Godolphin racing manager Simon Crisford said: "That was a great run from him and he's been a really busy horse over the last few months. All types of ground come alike to him and he's turning into a really nice horse.
"I thought he had won from where I was standing. Frankie (Dettori) said his whip was knocked out of his hand about a furlong out, but these things happen and fair play to the winner.
"That was a great run from ours too and he will head to Epsom now for the Diomed."
Ouch! Barry R