The John and Thady Gosden-trained four-year-old had a horror draw in stall 20, yet the Italian had the confidence to stay wide, all on his own, until they turned into the straight.
Evoking memories of Trawlerman's sire, Golden Horn, who stayed wide when landing the Prix de l'Arc de Triomphe, Dettori kept things simple and while he was passed by Earl Of Tyrone and then Alfred Boucher, his mount rallied in the last 200 yards.
Wednesday's winner Alfred Boucher made a gallant dash close home and had his head in front two strides from the post, but Trawlerman (9-1) kept finding to score by a short-head.
Earl Of Tyrone finished a length further back in third, while John Leeper was fourth.
Dettori said: "My colleagues gave me a little bit of rope. I managed to get him to relax and in the straight I thought I was beaten but the grey horse came and kind of helped me.
"I thought I was just running out of runway and I might not get there but on the line, in fairness, he dug deep, put his head down and I thought 'Ah! Close!'.
"In the past I've been close with Lady Aurelia (in the Nunthorpe) so I kept my mouth shut and I waited for the judge!"
John Gosden paid tribute to Dettori, whom he had a public falling-out with earlier in the season, which resulted in a week's sabbatical for the rider.
"I think when we went and walked the course before the Arc with Golden Horn, we saw how wide his draw was and Frankie said, 'I'm just going to stay out there'.
"We did it here with Muntahaa and Jim Crowley, who thought I was mad. I said it was a Baldrick plan that can work."
He added: "You have to have a very good owner who would understand if it doesn't work. If it doesn't come off, it doesn't come off. There is only one risk - if they go down the outside, they know where the stables are."
Of the public falling-out with Dettori, which was quickly addressed, Gosden added: "I could not get his attention - I could not get him to concentrate, that's all. In the end we gave him a bit of a public warning - that's the way it is. He was left on the bench like he would be by a football manager.
"He has just ridden two fantastic races today and when our man is in the zone he is absolutely top-class. When he is not in the zone, he is a menace!"